How much of you is you, and how much is from other people? That might seem like a weird thing to say, but in Uglies, there are lots of elements that go into making each person's identity. For instance, Tally may be a trickster—but maybe she's only that because the city society is set up to let her pull tricks. Or maybe she pulls tricks because she's friends with other uglies who like to pull tricks. Maybe she likes tricks? (It's so hard to know.) So lots of outside factors affect Tally's identity—and that's all before we get to the pretty surgery with its brain lesions, which seriously would affect her identity. In Uglies, identity isn't something stable and unchangeable, it's a growing part of who you are, affected by everything around you.
Tally finds her own identity by watching other people struggle with their identities (like Peris and Shay who get made pretty, or even Maddy and Az who have to give up their identities as doctors in the city to become runaways).
Individual identity in Uglies often conflicts with friendship, because friends often try to make each other over and change their identities.