Most Helpful Girl
I think maybe a discussion about what "serious" means is more important. I think this is the classic miscommunication in a lot of relationships. My ex boyfriend thought "serious" meant I was ready to get married. I thought "serious" meant we were in love with intentions only to be exclusive to each other in the foreseeable future.
Are you two exclusive? Acting like a serious couple? If so, I'd continue to go about things her way. It's possible the discussion freaks her out, but she's still your serious girlfriend. If you are still not exclusive at this point and she doesn't want to call you her boyfriend, I think it's time to move on. 6 months is long enough to achieve that level.