As with many changes on the site, this one should be considered "experimental" or "provisional". Throw it against the wall and see what sticks.
I'm soliciting opinions. My own is that "pope" is both too singular (very unique?) in that the Catholic Church only has one pope (except under extremely extraordinary circumstances),
and too specific to one particular religious sect. "Patriarch", on the other hand, is more generic, and is used by a variety of sects: there can be, and in fact are, numerous patriarchs in the world
at any given time.
Perhaps we should consider a term from other monastic traditions, such as... lama?