It actually changed prior to the release of Oblivion, they still went by gamesas when they released Morrowind.
EDIT: Or at least I think so, based on the fact that Bethesda Game Studios isn't mentioned on the box or during the opening credits of Morrowind, it just says gamesas. Maybe they called themselves Bethesda Game Studios internally though.
I duno, the wiki says BGS has been around since 85
http://en.wikipedia.org/wiki/Bethesda_Game_Studios
Perhaps they were an internal development team only recently broken off as its own things while still flying the banner of BS
Edit: never mind, all is answered.
"the studio's name and logo was established with the release of The Elder Scrolls IV: Oblivion in 2006."