Sokka and Katara know Ty Lee's name, but I'm not sure??if Aang and Toph do. Here's part of the episode transcript for "The Chase" after Mai and Ty Lee caught Sokka and Katara:
Mai: I thought when Ty Lee and I finally caught you guys (she slumps a bit and looks down in disappointment) it would be more exciting. Oh well, victory is boring.
(episode transcript is from Avatarspirit.net)