Notwithstanding whether or not the Glock should have been recorded prior to the 4473, I've had issues because of a common name. The ssn is optional, but I've never had a problem when I do fill it in.
I also have a very common name. In fact at one time 3 of "us" lived within 1 1/2 miles of each other. I always use my SS# when filling out 4473's because of the potential problem. Waited the full time out required, did not hear any more, and was allowed to pick up fire arm.