The Sage said:No it doesn't. In the comics, Connor is the name given to Superboy by either Superman or the Kents when he decides to live a civilian identity as CK's cousin. If you were to use my idea, Clark could name Superboy Connor in honor of his first teenage clone.
Thats repetitive though, and kind of silly when you think about it.
I think logically, (if you feel compelled to do the clone story this early on) you should use Bizzaro first. He's far less perfected than any type of Conner-like clone and pretty rough around the edges. Hes pretty much an experiment gone wrong.
Personally I wouldnt use either at this point in time, Clarks only 18. This stuff can wait till hes Superman. It doesnt do much, writing-wise, to show a teenage clone of Clark Kent, when Clark himself is still a conflicted teen. At least with Superman, the differences between him and Conner are pretty big.