My girlfriend asked me what she should call me and what to call me.

Well, that's easy to say. If you are at home, of course, you should call her husband or dear. If you are working, she can call you Lao Yang. If you are his boss, she will call you whatever others call you (such as Yang Zong). You should call her wife or darling. Needless to say, you should call him sweets at work. Is it vulgar? You can call her baby. It feels very kind. I hope I can help you.