Hi Jason,
There are couple of options with you on this migration and I will list down each:
- Option - Simple - During the cutover you can create a new DNS Record or Update the existing records in the DNS to point it to the new IP address and this can be either Onpremise DNS or if you are planning to provision Azure AD Domain Services as this will be sync with your Onpremise AD.Update production DNS entries for source servers to point to the new IP address in short that is 10.x.x.x address.
- Option 2 - Complex - Use Azure DNS private Resolver and detailed information is over here dns-private-resolver-overview, you do not need to create Azure AD Domain Services for this.
Note the TTL value of the DNS records should be less before the cutover so the clients refresh/resolve with the new entries and correctly resolve the address after the cutover.