While it’s nice that boyfriend is so concerned of making things easier for his mom, it seems that there is some reason he doesn’t want to introduce you as his girlfriend. It could be that Mom’s apron strings are very tight in this case, it could be that he’s not sure the relationship is going to last, it could be that Mom prefers someone else for her son, or something else entirely… OP, I would recommend asking boyfriend why he felt that way. Unless the explanation makes sense to you, I suggest that you realize that you are likely to come in second in boyfriend’s life after his Mom. Good for Mom (maybe), but ultimately not good for you, the relationship, or him. This may not be a “fixable” relationship if you want a close relationship.

he has another girlfriend. that's why he did not want to introduce you

Were you buying the car? If not, why bother meeting the mother?

I think you need to cut your losses. he should have introduced you a long time ago. he either can't stand up to his mom, or he has a main girl and you've been a long time side chick. either way is not fair to you. at this point you deserve a man that's proud of you.