Relationships have rules, roles, and most importantly, conflict resolution protocols. Here, you have a rule that you want him to observe that he is not observing despite you communicating about it. Now you’re looking for an appropriate escalation tactic to get him to respect the rule that doesn’t necessarily involve threatening or actually leaving him.
So, rules flow from roles. A role is how partners see each other in the relationship. If a guy is not telling a girl that you guys are together, then it’s not so much the fact that he’s not doing that that bothers you, it’s the idea that he doesn’t see the relationship the same way you do that really hurts.
So this is where you need to focus on when talking about him. Not about the behavior, but rather on the perception. How does he see the relationship? Are you guys casual or serious? You want a serious relationship, you’re really not sure how he sees it or what he wants.
So you have to nail him down on how he sees it. If you ask him and he says “oh I’m totally serious about this relationship” then you can say, “well something’s not adding up here because you didn’t tell that girl we were together.” Make him give you an answer about this, and make sure it’s a good one.
If he can’t give you straight answers, then he’s not being straight in his communications. That means he doesn’t take his relationship with you seriously. You should take it extremely seriously if he doesn’t take his relationship seriously with you, if that’s what you want and that’s what he’s led you to believe he wants too.
Good luck!