AFAIK He started work on the STL at HP and then SGI based on his and Musser's work on Generic Programming but it didn't get the name STL until he was at the STL.

This of course coming from Sean Parent who was and afaik still is quite close with Stepanov. Sean Parent of course being famous in his own right but also being notable for bringing Stepanov to Adobe and being the one to push for Stepanov to propose the STL to WG21 (the C++ ISO Std committee).