Two months is a perfect time for you to initiate a conversation. There are two of you in this relationship, and both of you have ideas of how you like to date, and how you want the relationship to be. Your job is to now see if he is on the same page as you. No matter how cute and fun he is, it's not going to work if he doesn't want the same things as you.
You want to be an exclusive couple. Of course you do. You wouldn't want him kissing other girls because you're not officially a couple. Your needs matter. This is what I would say to him, if I were you. "We've been dating for two months now, and get along really well. I want to know where you want to go from here. Are you the type of person who wants to be free to date a lot of people, or do you want to be exclusive?"
If he says he wants to be exclusive, great. If he says he wants to date a lot of people, then tell him you're not comfortable with that, and you'll have to move on. If a guy doesn't want you exclusively to himself, and wouldn't mind other guys dating you, then he's just not that in to you.
Some women have a habit of letting the guy set the pace and tone of a relationship. Always remember that you have feelings and a brain, and you need to do what's best for yourself. You're in the drivers seat. I hope he wants the same things as you, but if he doesn't, cut him loose so you'll be free when the right one comes along. Good luck.
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