AWS offers its route 53 domain name service. It doesn't care where the host is - you setup the DNS records and it will point to them.
I happen to have my DNS at AWS route 53 and web server there as well, but you don't have to.
In fact, you can have your domain registered at company 'A', nameservers handled by company 'B' and the website can be at company 'C' - there is no requirement that they are together, and in fact there are lots of good reasons not to put all your eggs in one basket.