Over the years, I used No-IP to link a domain to my IP address, and then used No-IP's DUC (Dynamic Update Client) to update my IP, so that the domain will always point to my IP.
That's very handy for running dedicated game servers.
Is there a DUC-equivalent for Google Cloud DNS?
In essence - No - there isn't :(
Unless yo're using Google Domains for your domain hosting then yes - they support just the thing.
Cloud DNS doesn't have that functionality. There are several workarounds like reserving a public IP for your VM which in my opinion would be the best way to do it. Unless your VM get's deployed using Deployment Manager then it may require some more scripting.
Similar questions have been raised on Stackoverflow here and here which you might find helpful.
If you're running Linux here you'll find a complete script how to update DNS records after a machine startup.
