Simple answer to a simple question: There is no separate registration for IPv6 vs. IPv4 addresses with regard to DNS domains.
You own your DNS domain. There is no separate DNS name space for IPv4 and IPv6 domains. That is, a DNS domain is a DNS domain, and whether is points to an IPv4 or IPv6 web site is dictated by what you put in the domain. No one can register an "IPv6 version" of your domain, because that doesn't exist. DNS domains and the IP version your web site runs are independent of each other.
If you want to add IPv6 to your web site, you simple configure IPv6 on your network and web site. At that point your web server will accept requests over IPv6. Now you can simply add an IPv6 AAAA record to your domain name entry, and your web site will have an IPv6 address in the DNS.
For example, if
www.abc.com had an IPv4 address of 192.0.2.10, it would have an A record looking like this:
www.abc.com IN A 192.0.2.10Now, if you set up IPv6 on your server and network, and added the IPv6 address "2001:db8:1234:10" to the web server, and wanted the site to also be accessible via IPv6 in addition to IPv4, you'd add an AAAA record:
www.abc.com IN AAAA 2001:db8:1234:10
That's it. Now your web site has both IPv4 and IPv6 access.
Some people prefer to keep the IPv4 and IPv6 domain names for their servers separate for various reasons. Typicaly, this is done with a subdomain. So for instance, you could create a subdomain called "ipv6.abc.com" and put all your web sites in that (for instance
www.ipv6.abc.com), and keep all the IPv6 AAAA records in that subdomain. No one can steal that subdomain from you either, since it's part of the parent domain you own of course.
Additionally, DNS doesn't care whether it's running under IPv4 or IPv6 to return IPv6 resource records. In other words, a DNS server which is using only an IPv4 address can serve up IPv6 AAAA records and the ip6.arpa reverse domain just fine. Likewise a DNS server which has only an IPv6 address has no problem serving up any type of resource records including IPv4 A records. Right now it's best to run both an IPv4 and IPv6 on ones DNS server to provide universal access.