The name of the first game is "The Precursor Legacy", and the franchise in general, being "Jak and Daxter". After all, the PSP game is also called Jak and Daxter, but the specific title is called "The Lost Frontier". Also, do not forget that the entire trilogy released for PS3 is referred to as the "Jak and Daxter Collection" and "The Jak and Daxter Trilogy".
Besides, she was introduced in the second game too. >.>
But yeah, based on the original trilogy, Jak II and Jak 3 is what I designed my Tess cosplay on :3
I could seriously play these games for forever. I might just have to get the PS3 trilogy since my original backwards compatible PS3 died, boo I still have my PS2, but couldn't hurt to have the whole trilogy in HD either