One of the more persistent rumours about the meaning of GWAR is that it comes from the graphic novel Watchmen by Alan Moore and Dave Gibbons. In that book, GWAR is an acronym for Gay Women Against Rape, the name of a protest organization whose posters can be seen around New York in many frames. The posters, distributed by a butch lesbian called Joey, advertize a benefit concert at a venue called the Pink Triangle, and the initial letters of each word are enlarged and highlighted, drawing attention to the acronym. In a later scene, the poster is shown torn, so that only the letters WAR can be seen.
The band have given this explanation in certain interviews, and in their movie Phallus in Wonderland there is a scene in which protesters hold up a Gay Women Against Rape sign, so they are definitely aware of the connection. On the other hand, they seem to delight in giving contradictory explanations, so I'm not going to try to claim that this is the 'true' derivation of their name.
eponymous wondered whether GWAR predated Watchmen, however the chronology seems to fit, as Watchmen was first published in 1986 and GWAR released their first album in 1988.