Your significant other should accept your flaws and find ways to help in whatever way you need (which in your case may just be patience and acceptance). My stutter is primarily blocking which prevents me from saying things (especially when excited, mad, nervous, embarrassed, stressed, etc). Communicating during these times can be very crucial to a relationship’s health. My wife is exceptionally patient and understanding that I can’t say things that I might need during these times. Somebody could say I stutter during these times to get out of talking about things or to get pity. Luckily my wife is not one of those people and that is just one of the many reasons I love her. I don’t think I could be with someone who didn’t 100% love me for me and that includes my stutter. It’s not something you should need to me worried about or embarrassed about to your significant other. I’m not going to say leave her but I am going to say that having a significant other accept you and help you is going to make for a much happier life. It’s especially great when your significant other handles introductions because they know you have troubles saying your own name :) Hope the best for you and that you and your girlfriend can get through this situation! You deserve someone who 100% understand and accepts you.