Stutterer; do I tell my bf?

Stuttering has been such a hard thing to deal and face with in my life. It’s stopped me from being confident, having friends and constantly so hard to talk without hesitating almost every time I want to speak. The first time I met my boyfriends mom, I couldn’t do it, I stayed in the room until we left. She asked him if I was okay because I didn’t talk. This past weekend I met his friends and for the life of me could not say what my name was 3 different times. Twice my bf was there, although he didn’t say anything he looked at me like are you gonna say your name? He’s such a sweet and genuine guy who doesn’t judge or criticize anyone which I love about him and I’m sure he’d understand but stuttering is so hard for me to let anyone know about. It’s not something people really know about me because the way it embarrasses or how much it does is just… sucks so bad. I’ve struggled with jobs because I can’t answer the phones for interviews and there’s not much jobs for me to do where I’m able to not talk to people which would be a dream but that’s not how it works. My bf currently wants me to go to a trader school to further my career as the same thing he’s doing. It’s a field that we both love and he told me today to call to schedule orientation and I can’t do it. I would love to do the same thing he does but there’s a lot I’d have to do to to talk with people and I can’t. I want to confine it in him to share this but I’m so disappointed and ashamed in myself. The thing for me is I don’t want to ever let anyone know how badly I struggle talking, how much I struggle and hesitate to speak one word such as my name, I can’t let anyone know because it’s that bad.