How do I prove to this guy that I really like that I'm a changed person, and not promiscuous anymore?

I really like this guy and I know he likes me too cuz he told people that he did, but apparently someone is telling him about stupid things I've done last semester that are over and done with. I know I'm not a slut anymore at all, but people still bring up the stuff I've done in the past, specifically to this one guy that I really like. I know he wants a relationship because he told his friend that, and I want one as well, but I am afraid all this talk about my past mistakes will cause him to not want a relationship with me...What should I do?