He doesn’t refer to me as his girlfriend to others

We’ve been dating for roughly 6 weeks now and agreed to be exclusive about 2 weeks ago. Idk if it’s cuz we’re still new to the relationship, but he doesn’t introduce me as his gf to his friends, only says that we’re dating and my first name. I kept quiet but it’s making me double guess a lot of things…am I overthinking? I figured a guy would be proud to show you off as his gf?? I know I am that way, but now I’m double guessing on whether or not to even call him my bf if he isn’t doing the same? Thoughts??? I don’t want to come off over bearing by point blank asking why, but it feels like a situation where’s it’s awkward to even speak up??