I don't see, and haven't found in narrative, or even in limited reading of out-of-narrative information, any information confirming that this is a proper name.
As it's been 4 days, and Czechout agrees this is open to interpretation without further information (which I take to mean that it is a speculative name), I'll proceed to remove specific references to "Anglican Marines" or "Anglican Regiment" as the proper name of a group. Where appropriate, I'll replace the information that marines who are Anglican are part of the Church presence.
Czech, if I'm overstepping or if later disagreement or confirmation shows up, the edits could be reverted easily enough.