Jefferson Airplane split into two groups: Jefferson Starship and Hot Tuna
Jefferson Starship were the singers (Grace Slick, Marty Balin) and rhythm guitarist (Paul Kantner). Kantner owns the "Jefferson" part of the title, so when he left, they just called themselves Starship. BTW the "Jefferson Starship" title refers to the original super-group that formed to play on the "Blows Against The Empire" album. It included members of the Grateful Dead, Jefferson Airplane, and David Crosby. Later, after the Jefferson Airplane broke up, Kantner used the name to form a new band.
The lead guitarist (Jorma Kaukonen) and bass player (Jack Casady ) formed Hot Tuna. They were the musical core of the group. Jorma is one of the best rock/blues guitarist to ever play. Hot Tuna plays epic shows lasting 5 hours with no break. They are still touring and are a must see.
Read the link about the Matrix Club, the SF hangout where everyone gravitated in the '60s