Switch PlayerName writes to Outfit

Switch PlayerName writes to Outfit

In 2024.6.18 Innersloth changed the storage location of the PlayerName
from PlayerInfo to PlayerOutfit. If we don't set the PlayerName, we'll
send an incomplete PlayerInfo to new players, so new players are unable
to stay connected as they will not receive complete PlayerInfo objects
before a timeout in the client activates.

Because we publish PlayerName in the API, we can't completely remove
the PlayerName field from PlayerInfo. We also use it internally in a few
places, so I don't this is worth removing.