Long answer: The status screen is as visible to any given character as their player wants it to be, by which I mean the character basically has no control over what other people see in their status screen, but if you wanted to play a character who couldn't see status screens (or player names) you could.
If a player actually did say they had a problem with canon puncturing ((IIRC no one has as of yet, yay)) then I would probably not overtly mention their player name ICly, but I see no reason it wouldn't be visible.
I probably could have explained this more clearly ... >_> If that didn't make sense please don't hesitate to say so.
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Long answer: The status screen is as visible to any given character as their player wants it to be, by which I mean the character basically has no control over what other people see in their status screen, but if you wanted to play a character who couldn't see status screens (or player names) you could.
If a player actually did say they had a problem with canon puncturing ((IIRC no one has as of yet, yay)) then I would probably not overtly mention their player name ICly, but I see no reason it wouldn't be visible.
I probably could have explained this more clearly ... >_> If that didn't make sense please don't hesitate to say so.