Origin Systems's in-house bible referred to him as "Bluehair", a joke about the artistic usage of blue highlights over his dark hair, a result of the lighting of the Tiger's Claw. The default name of the character by the program (eg. when jumping missions by a cheat) was "Bluehair" Our Hero
Early developmental material called him Arturo Blair (from Our Hero Bluehair), and Falcon for WC1 who would become Phoenix in WC2.
With the shift to full-motion video and pre-recorded speech in Wing Commander III, a set name was needed. Bluehair became Christopher Blair, taking his name from Wing Commander creator Christopher Roberts. A Blair appeared in Freedom Flight previously, but there is little evidence that the character was tied to Bluehair.
Other media have used different names. Wing Commander I & II: The Ultimate Strategy Guide used the name Carl T. Lafong and Pitak Puzaki (for two systems). Super Wing Commander and the Sega MegaCD port of the original Wing Commander, which also used full speech, named the character Jason Armstrong and Lyle Starbuck, respectively.
Star*Soldier makes at least Christopher Blair, Carl LaFong, and Jason Armstrong each separate individuals who happened to serve on the Tiger's Claw, etc, and shared similar missions. LaFong and Armstrong at least released memoirs of their own lives The Memoirs of Lieutenant Colonel Carl T. LaFong/Wing Commander I and Super Wing Commander respectively.
In LaFong's journal the first two games are treated as a simulator of the events made up of composite characters and stories from many different sources and POVs, and what-ifs to allow for both winning and losing situations.