If it's not traceable to a legally licensed maker it would be illegitmate, no? If it was stolen and used in say a crime then how would that serial number be traced if it wasn't registered somewhere?
In the United States, per federal law (meaning that if you live in a communist state things might not be as favorable) you may manufacture any sort of firearm that you could otherwise legally own, for your own use. There is no requirement for you to mark it with a serial number or any other marking. That much is black and white, clarified many times over by the BATFE.
If you want to sell / give away such an article, you enter a gray area which basically boils down to intent: did you intend to get rid of said arm when you made it? That would be illegal. If not, it's not illegal. Hard to prove either way.
As I mentioned earlier, there is no requirement (federally) that you mark your home firearm in any way shape or form. However, it'd be dumb not to - having an identifiable marking can only work in your favor in the event of theft. It's not like you have to tell anyone (federally) what that serial number is until you want to. However, as soon as you want to transfer said Title 1 arm through an FFL it will have to have all the federally requisite markings - serial number, manufacturer's name, city, state, maybe some other stuff I don't recall, all engraved at least 0.003" deep and in a font larger than some specified minimum. That's because your FFL will have to fill out some of that information in their forms. You can legally mark it with your (you being the maker) name, city, state, and serial of your choice and that will suffice.
Which is a long way of saying it is absolutely legitimate to make and own a firearm that isn't traceable to a licensed manufacturer (said license being only necessary to manufacture for the purpose of sale).
All that is federal law. State law may impose additional restrictions. Most states do not, but a few do.
GsT