I just recently came back and realized you can swap pet names now. Does this preserve the "Legacy" name and just transfer it over, or does it essentially remove it? Thanks!

Neither. The legacy name is permanently attached to the pet that has it, so if you swap, e.g. Bob and Luke, both with legacy names, you'll have Bob (Legacy name Luke) and Luke (Legacy name Bob)

You can permanently clear the legacy name of any pet you want at the Bathhouse cleansing pools or hide the legacy name from their profile if you want to swap names without clearing them, in case the mismatched legacy names don't work for you