A least they changed it so it's Server specific. Originally they intended it to be cross-server.
I don't believe it was ever intended to be cross-server. The original announcement on the pre-wipe forums said that it was cross-server by accident, and it was quickly changed.
what level were you when you got to get your legacy name?
said, it's after you finish Chapter One (Alderaan and a small amount of content after the planet). Average level is probably low-to-mid 30s. Other than skills, there isn't much in this game that's tied to level - it's all tied to story beats, which different people will finish at different levels.