Soo .. what if we set up a TLD for families (in general), have each family of today register a name, then have each child register a subdomain for their prospective family, have each grandchild register a subsubdomain for their family, and so on. You'd create a family-tree-domain-system. Names would get pretty impressive.

Only downside: it'll be sparse and deep, which is rather counter-functional to DNS.