The easiest way to deal with this is for the players involved to agree on a ship naming convention that differentiates between them, like their empire's initials.
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Cap'n Q
"Good morning, Pooh Bear," said Eeyore gloomily. "If it is a good morning," he said. "Which I doubt," said he.
I don't know, I'm assuming that this is a problem for me and me alone. I'd rather not put my issued onto the other players.
Out of curiosity, does anybody know if a double-shipset assignment in a PBW game is something that affects all players when it occurs, or is this something that only one player has to deal with?