It's a timely question and an important one not least because it points to the responsible nature of ecclesial vocations. The first thing to remember is that if one claims to be a Catholic hermit, that is, one who lives an eremitical life in the name of the Church via profession (always a public act) and consecration, then one has been commissioned to live a public ecclesial vocation. If one claims the title "Catholic Hermit" or "consecrated hermit", etc., in creating a blog or other website, for instance, then one really doesn't have the right to remain entirely anonymous any longer. This is because people who read the blog have commensurate rights to know who you are, who supervises your vocation, who professed and consecrated you and commissioned you to live this life in the name of the Church. If they have concerns with what you write, they must then be able to contact you and, if really necessary, your legitimate superiors.
Ways of Maintaining Appropriate Accountability:
One thing that is possible, of course, is to say that this blog (etc) is the blog of a "Diocesan Hermit of the Diocese of Oakland," for instance, without providing one's given name. In doing so I would still be maintaining accountability to the Church for this vocation and what comes from it. If there is ever a serious concern, then the Diocese of Oakland (for instance) will know whose blog is being referenced. (In this case, they may not ordinarily concern themselves with my everyday writing because they do not micromanage my activities --- my delegate would tend to know more about my blogging, I think --- but they will know whose blog this is and deal appropriately with serious complaints or concerns that might arise.) However, it seems to me one still needs to provide a way for folks to contact one so the chancery isn't turned into the recipient of relatively trivial communications which are an actual imposition. (I, for instance, do not usually provide my hermitage address, but people who prefer not to email may write me at my parish. This would work even if I did not give my name but used "Diocesan Hermit" instead because the parish knows precisely who I am and provides a mailbox for me.)
A second solution is to blog or whatever the activity without claiming in any way to be a Catholic hermit, Diocesan hermit, consecrated person, professed religious, etc. As soon as one says I am a Catholic Hermit (or any version of this) one has claimed to be living a vocation in the name of the Church and the public writing one does, especially if it is about eremitical life, spirituality, etc, is something one is publicly accountable for as a piece of that living. So, the choice is clear, either write as a private person and remain anonymous (if that is your choice) or write as a representative of a public vocation and reveal who you are --- or at least to whom you are legitimately accountable. Nothing else is really charitable or genuinely responsible.
Some may point to books published by an anonymous nun or monk, books published with the author "a Carthusian" (for instance), as justification for anonymity without clear accountability, but it is important to remember that the Carthusian Order, for instance, has its own censors (theologians and editors) and other authorities who approve the publication of texts which represent the Order. The Carthusians are very sensitive about the use of the name Carthusian or the related post-nomial initials, O Cart., and they use these as a sign of authenticity and an act of ecclesial responsibility. (The same is true of the Carthusian habit because these represent a long history which every member shares and is responsible for.) The Order is in turn answerable to the larger Church and hierarchy who approve their constitutions, etc. Thus, while the average reader may never know the name of the individual monk or nun who wrote the book of "Novices Conferences" for instance, nor even know the specific Charterhouse from whence they wrote, concerns with the contents can be brought to the Church and the Carthusian Order through appropriate channels. This ensures a good blend of accountability and privacy. It also allows one to write without worrying about what readers think or say while still doing so responsibly and in charity. Once again this is an example of the importance of stable canonical relationships which are established with public profession and consecration --- something the next section will underscore.
The Question of Pride:
It is true that one has to take care not to become too taken with the project, whatever it is, or with oneself as the author or creator. With blogs people read, ask questions, comment, praise, criticize, etc, and like anything else, all of this can tempt one to forget what a truly tiny project the blog or website is in the grand scheme of things. But, anonymity online has some significant drawbacks and a lack of honesty and genuine accountability --- which are essential to real humility I think --- are two of these. How many of us have run into blogs or message boards that lack charity and prudence precisely because the persons writing there are (or believe they are) anonymous? Some of the cruelest and most destructive pieces of writing I have ever seen were written by those who used screen names to hide behind.
Unfortunately, this can be true of those writing as "Catholic Hermits" too. I have read such persons denigrating their pastors (for supposedly having no vocations, caring little for the spiritual growth of their parishioners, doing literally "hellish" things during Mass, etc), or denigrating their bishops and former bishops (for whining, lying, and betraying the hermit to the new bishop) --- all while remaining relatively anonymous except for the designation "Catholic Hermit" and the name of her cathedral. How is this responsible or charitable? How does it not reflect negatively on the vocation of legitimate Catholic hermits or the eremitical vocation more generally? Meanwhile, these same bloggers criticize Diocesan hermits who post under their own names accusing them of "pride" because they are supposedly not sufficiently "hidden from the eyes of" others.
Likewise, over the past several years I have been asked about another hermit's posts which have left readers seriously concerned regarding her welfare. This person writes (blogs) about the interminable suffering (chronic pain) she experiences, the lack of heat, and the serious cold she lives in in the Winter months which causes her to spend entire days in bed and under blankets and that left her with pneumonia last Winter; she writes of the terrible living conditions involving the ever-present excrement of vermin --- now dried and aerosolized, holes in walls (or complete lack of drywall and insulation), continuing lack of plumbing (no toilet) or hot water despite her marked physical incapacities, the fact that she cannot afford doctors or medicines or appropriate tests and may need eventually to live in a shelter when her dwindling money runs out. Unfortunately, because all of this is written anonymously by a "consecrated Catholic Hermit" presumably living eremitical life in the name of the Church, it raises unaddressable questions not only about her welfare but about the accountability of her diocese and the soundness and witness of the contemporary eremitical vocation itself.
This poster's anonymity means that those who are concerned can neither assist her nor contact her diocese to raise concerns with them. Here anonymity conflicts with accountability. While it is true diocesan hermits are self-supporting and have vows of poverty readers have, quite legitimately I think, asked if this is really the way the Church's own professed and consecrated hermits live. Does the Church profess and consecrate its solitary hermits (or facilely allow them to transfer to another diocese) and then leave them to struggle in such circumstances without oversight or assistance? Is this the kind of resource-less candidate the Church commissions to represent consecrated eremitical life? Would this be prudent? Charitable? Is it typical of the way consecrated life in the church works? Does a hermit's diocese and bishop truly have or exercise no responsibility in such cases? How are such hermits to be helped?? Unfortunately, the combination of this poster's relative anonymity and her lack of accountability, prudence, and discretion can be a serious matter on a number of levels.
In other words, while pride may be a problem (or at least a temptation!) for those of us who blog openly, it may well be that anonymity itself may lead to an even greater arrogance whose symptoms include writing irresponsibly and without prudence, discretion, or real accountability. Thus, anonymity can be helpful so long as one still exercises real accountability. Importantly, one needs to determine the real motives behind either posting publicly or choosing anonymity. Simply choosing anonymity does not mean one is exercising the charity required of a hermit. It may even be a piece of a fabric of deception --- including self-deception. For instance, if one chooses anonymity to prevent others from learning they are not publicly professed, especially while criticizing the "pride" of diocesan hermits who choose to post openly, then this is seriously problematical on a number of levels.
At the same time, some authentic Catholic hermits choose to let go of their public vocational identities for a particular limited project (like participation in an online discussion group or the authoring of a blog) and write as private persons. This is a valid solution --- though not one I have felt justified in choosing myself --- because one does not claim to be a Catholic hermit in these limited instances. And of course, some of us decide simply to be upfront with our names, not because we are prideful, but because for us it is an act of honesty, responsibility, and charity for those reading our work or who might be interested in the eremitical vocation. The bottom line in all of this is that anonymity may or may not be a necessary piece of the life of the hermit. For that matter, it may be either edifying or disedifying depending on how it protects an absolutely non-negotiable solitude or privacy and allows for true accountability or is instead used to excuse irresponsibility, disingenuousness, or even outright deception.
Summary:
The hiddenness of the eremitical life is only partly that of externals. More importantly, and much more centrally, it has to do with the inner life of submission to the powerful presence of God within one's heart. Sometimes that inner life calls for actual anonymity, and sometimes it will not allow it. Since the vocation of the Catholic hermit is a public and ecclesial one, any person posting or otherwise acting publicly as a Catholic hermit has surrendered any right to absolute anonymity; they are accountable for what they say and do because they are supposedly acting in the name of the Church. The need for and value of anonymity must be measured against the requirements of accountability and charity.