From a 2003 interview with Bobby Golden, one of the founders of the band, that can be found here
Luc Brunot: One last question. You certainly know that Cameron Crowe, in his movie "Almost Famous" gave the name of Stillwater to the rock band which is the center of the film. Did he contact you and sign an agreement and are there facts referring to the real Stillwater's life style? The director is a fan of Southern rock and did he made many allusions to the Allman Brothers and Lynyrd Skynyrd, all through all the movie.
Bobby Golden: I lived and worked in Italy when I received a part of the rights paid by Dreamworks to Stillwater to have used the name of Stillwater in the film "Almost Famous". After having called at house to know why I touched these rights, I discovered that the company of Steven Spielberg, Dreamworks, had contacted Sebie Lacey, our singer to establish a deal concerning the use of the name. The young Cameron had seen us in the seventies, in Macon, Georgia, at the time of a concert organized by Capricorn Records, whereas he wrote in Rolling Stones. Even if the film is not devoted to us, it remember me some good memories of our ten years of tours and recordings when we were. almost famous.