I’m not sure if you met on Tinder and if you took your profile down and he didn’t, but at two months, he probably wasn’t ready to be exclusive, or he would have said so.
When a man wants a woman to be his, he does what it takes to make her is girlfriend.
Something is also wrong in your relationship if you feel you need to check up on him. I can’t say if it’s a deal breaker for you, but as soon as you tell him you’ve busted him with a fake Tinder profile, or make up a white lie and say that someone found him on Tinder, I guarantee he will break up with you. My boyfriend – who is over 60 – has had more dates than anyone I know and still receives notifications of women who have emailed him constantly.