I didn't downvote you, but, on the surface, your question is nonsensical. A registrar provides only one useful service - "Identify what the DNS servers for this domain are." That's what you pay your annual fee for, so, to ask "does name cheap let you do your own name server on your own domain for free" doesn't make sense to most people.

Indeed, it's the _inverse_ that is somewhat rarer, which is providing DNS services for a domain for free. Not all registrars provide free DNS services in addition to being a registrar.