Hello , is your last name a common name? if so this may not be a problem in the end. However ,as you are doing now ,it would be wise to address the issue prior to filing. There are several ways to do so. I am sure other members will chime in . IMO, Submit with your I-129F packet Birth certificates for both you and your fiancée. You can also submit BC's of both parents if available. I don't think your embassy is a tough one ,I may be wrong. In the end if your CO suspects you may be related as lets say cousins ,a DNA test may be asked for.
Side note: It is not illegal to marry a cousin if the state you are residing in allows it.
On the i-129F there's specifically this question:
"Is your fiance(e) related to you?"
Check no, and be ready to show proof if requested (I don't think they will ask for it if the surname is common, but I might be wrong).
