When do you define a relationship?

I’ve been dating a guy for a month now, but he hasn’t asked me to be his girlfriend. Earlier in the relationship he said that he would love to call me his girlfriend, but I said I was scared that we would fizzle out since it had only been a week. He said that he understand and that we could check in in a week or two and see where we were at then. Two weeks have passed and we haven’t had that check in. We hang out once every week and text everyday. I want to be his girlfriend, but idk if I should bring it up? Help.