You don’t need to. Your registrar tells the registry which nameservers you’ve chosen. You specify the nameservers that belong to your DNS provider, which causes DNS clients to query that DNS provider.

There’s nothing stopping you from paying for service with a DNS provider for a domain you don’t own, but nobody will actually query those nameservers for your domain, so it doesn’t matter.

You usually need to update the name servers with service A to point to service B.