Is it possible to automate DNS record update upon a failover to a replica VM?

We have two Hyper-V VMs, both running Windows Server 2012 R2. One is a replica of the other, replicated over server farms using Hyper-V Replica. They share the same hostname, but have different statically assigned IP addresses, network ID and host ID both distinct. Let us call these IPs ip1 and ip2.

Upon an unplanned failover to the replica VM, is there any way to automatically update the DNS record 'myserver -> ip1' to 'myserver -> ip2', without any manual operation. We did a little testing in our yard, and had to manually update the record,
so we have been wondering if this is due to our faulty configuration or by design.

We are on a closed network (i.e. no Internet connection), and everything, all the client PCs and server farms, is in a single domain.