Wow, such great questions!! And yes, your analysis is pretty much on point -- with some nuances and expansions to be added. Also, of course you can come back with more. I'll email you this first answer and then you can reply with more. How does that sound?
So, ordinarily the rights and obligations identified as part of an ecclesial public vocation have to do with representing the vocation one has been commissioned to live in the Church's name and to do so well. The obligations refer to living the vows well, understanding, valuing, and conveying the nature of c 603 similarly, living one's Rule and the values that comprise its central elements well, and I would say particularly, giving evidence that one lives the Gospel of God in Christ in a way that convinces people that God really is of primary importance to oneself and also to any really compelling spirituality one holds.What I was given in exchange was the right to identify myself as a diocesan hermit, a member of the consecrated state in an ecclesial vocation bound publicly by the Evangelical Councils and a Rule of Life I had written and that was vetted by canonists and approved by the Bishop professing me. I was also given the right to style myself as a religious Sister, to wear a habit with my bishop's approval and a monastic cowl (after perpetual profession only). In other words, I was given the right to call myself a consecrated Catholic hermit who lives this vocation in the name of the Church. A year after perpetual profession, I was also given permission to use the post-nominal initials Er Dio as part of my signature indicating my identity as a consecrated c 603 hermit. And, although I have not used this right (and likely can't do so the way some might be able to), I was given the right in civil law to set my hermitage up as a 501(c)3 religious house. So, with that out of the way, let's get to your questions.
The Questions:
Yes, I would agree that if you found me posting bad theology you might eventually be required to contact my diocese, particularly if I had not been sufficiently responsive to your attempts to speak with me directly. Let me point out, however, that I should be culpable for something serious here and not a matter of a simple theological disagreement. And yes, you are right about the importance of my providing a way to reach me or my diocese so long as I claim to be a diocesan hermit. Part of the obligations I accept in claiming a public ecclesial vocation is a certain relinquishment of the right to absolute privacy. If I am going to express myself publicly and represent myself as a diocesan hermit, people should be able to verify my bona fides. That ordinarily means folks have a right to know my name, as well as the date and diocese of my consecration. If I should want or need to withhold my name for safety's sake, but still choose to express myself publicly, then I must identify the diocese to and through which I am responsibly professed. This would not be optional because my vocation is a public and ecclesial one. (Please also see, OnAnonymity and Accountability in c 603 Vocations )As noted above, the right to claim an identity as a diocesan hermit comes with correlative obligations. This vocation, as ecclesial, is about more than just me and God alone. People in the Church and larger world have correlative rights and legitimate (valid) expectations re a consecrated person in the Church. This is one of the things new candidates for profession have to be helped to understand. It is not just that one can now be identified as a diocesan hermit. That right comes with correlative obligations to all whom one's life as a hermit touches! I am responsible not just for what I say or do; I have obligations to others to be who I say I am and that includes being transparent about my identity and canonical bonds within the Church. If I claimed to be a diocesan hermit and yet refused to provide my name or at least my diocese, then it would be a betrayal of the public and ecclesial nature of the vocation. The only way to remain anonymous would be to also refuse to claim an identity as a diocesan hermit; in such a case, however, one would be emptying a God-given public and ecclesial identity of any real meaning.
How About Carthusian Monks signing "A Carthusian?"
So what about the Carthusian monks whose books are signed "A Carthusian"? (I'm pretty sure they use this more than they use "anonymous.") Strictly speaking, they are neither remaining anonymous nor refusing to be transparent. They are providing the name of the Order they belong to and that Order is the responsible party here. That Order is publishing in a way that makes the entire congregation responsible to the Church and larger world for what is being published in their name. And that is the key to the situation, being responsible for what one says or does and who one is in the Church and larger world. But c 603 hermits do not belong to an Order. They are diocesan hermits, hermits admitted to public standing by a diocesan bishop and responsible to the People of that local Church as well as the larger Church for this public vocation. Can they remain anonymous? Yes, once professed, they could choose to make this part of their eremitical hiddenness (though it need not be). But let's be clear, they could not do that AND violate their chosen hiddenness by public expressions (blogs, videos, articles, publications) as a diocesan hermit! One simply cannot claim anonymity AND a public ecclesial identity at the same time. That is inconsistent, dishonest, and disrespectful of those to whom one is writing or speaking, as well as to the diocese that has entrusted one with this vocation.On the internet, I sometimes find folks who insist on remaining anonymous and often tend to be dishonest, exploitative, and selfish. It is striking to me that they are free to publish almost anything they want, truth be damned, if that is what they desire, and they do it in the name of freedom. (It is really about license, not authentic freedom!) Were a c 603 hermit to claim anonymity while at the same time claiming to say or do what they say or do as a diocesan hermit, they would especially not be able to justify this claim in terms of eremitical hiddenness. Again, it would instead be an act of irresponsibility, perhaps even cowardice, and it would certainly fail to respect the persons who listen to or read their works. The only place this might be acceptable might be a situation where a journal (for instance) had taken responsibility for the quality of the hermit's published piece and the author's bona fides. But again, in this situation, as in the example from the Carthusians, someone is taking appropriate responsibility for readers, listeners, et al who have their own rights.