To use your own domain name, you will need:
- Azure DNS Resolver
- Private DNS zone (assume you would already have this) that is linked to the resolver.
Then the DNS IP gets directed to the Azure DNS Resolver, which does a lookup on the Private DNS Zone.
I setup something very similar here: https://luke.geek.nz/azure/azure-point-to-site-vpn-and-private-dns-resolver/