If this should become a feature, please make it optional (default off) for those wishing a bit of privacy.
In the forum, there's already something called "Show others my online status" under Profile -> Account Settings.
If you uncheck this, you will appear as a Hidden User under "Who's Online" - so nobody can see your name.
We could do something similar for the transcribing, I guess - just have it say "1 hidden user is transcribing this ship" or something.
That way, those wanting privacy will get it, but other transcribers will still know what they need to know.