Embarrassed that I stuttered introducing myself to my girlfriend’s family

Embarrassed that I stuttered introducing myself to my girlfriend’s family I’m a 20 year old female in a relationship with my 22 year old girlfriend, who I adore and am very happy with. On Easter she brought me to meet her extended family (I already met her immediate family) and well... I had an absolute block when I tried to say my name. I went “hi, I’m.....” and my name would not come out. It was the worst thing and everyone there was listening so it’s not like only one person heard it, everyone heard it. My girlfriend’s mom actually had to say my name for me. It was awful. Afterward my girlfriend even repeated what happened and mimicked my block back to me, which just made things worse. I don’t stutter much around her so I don’t think she’s picked up that I have one, and I haven’t told her I have one cause it’s embarrassing to talk about, at least to me. So anyway I completely fucked up meeting her family and I wanna cry every time I think about it. I just keep thinking that they all think I’m some loser or some idiot, when I’m not and I just have a stutter. Anyway I guess I’m just looking for support and to see if anyone else has had this happen. Thanks in advance