They where oringinally called Jefferson Airplane in the mid to late 1960's. When they re-united in the late 70's or early 80's they changed the name to Jefferson Starship.
Starship was a different band with the Jefferson Starship's co-lead singer, Mickey Thomas.
The band was originally called "Starship" but it has been Jefferson Starship since 1992.
briefly looking at Wikipedia has failed me again.