Question about Player IDs

Are Player IDs ship wide? Meaning, if I have the Player ID name :Isaac: does that mean none of the other ship can use that Player ID name? I appreciate it if someone can shed some light on this question.

The Player ID is cross-ship, I thought. It is essentially the PN number you start with that you can change once for free. It will be what shows up in player communications and such as a unique identifier for a player.