Tim never officially assumed the name Skullfire in the original 2099 series. It prominently appeared on the cover of X-Men 2099 #7 and various supplemental sources, but was never used in the comics themselves, even in caption boxes.
Tim Fitzgerald turned into a being of pure energy at the end of the X-Men 2099 series, #34-35. He did not appear in the sequel series, 2099 World of Tomorrow. In the new 2099 timeline from Spider-Man 2099: Exodus #5, he's back in a human form (and called Skullfire).
His middle names, Sean and Michael, were revealed in X-Men 2099 #1 and #31 respectively.