I started seeing a guy with the same last name as my mothers maiden name, but there are 2 different families with that name here. When we first met we asked if we were related and our parents didn't know any of the name we said so we figured we weren't related. We're now seeing each other and just found out that his grandfather is my great grandfathers cousin. What does that make us? Should I stop things with him now?

Legally, you are fine. However, you may want to factor in how your family will react.

No, its not OK to sleep with your 6th cousin because you aren't married. No one should be engaging in sexual intercourse unless they are ready to have a child.

However, there is no legal or genetic problem in your having a relationship with him, that might lead to marriage.