When porting old games from D3D -> OpenGL, it's very useful to understand what type of coordinate system you're using. I think pushing this information into the function names could be useful.
GLM supports all these variations. However, even if you decided to support "the one true way" (whatever way that is hehe), then at least being clear about what that one way (is in the function name) might be good.
Note, this is not a feature request to support all these alternate coordinate systems, if you don't already (browsing the source, I think not?). If that were interesting, I think it should probably be a separate ticket.