DNS in CloudSQL wth private IP

How do we set DNS in CloudSQL wiith private IP only. I am using the server cert from the CloudSQL instance but get the following error when using the private IP in nodejs code.

 Understand the the private ip can be assigned a domain name but I have the following concern

1. I don't own any domain, how do we use Cloud DNS to get a google domain subdomain or equivalent?
2. PrivateIP will change when Instance edited i.e. when Network is changed, then Cloud DNS would point to wrong IP.
3. As per the above error message its not clear which domain the certificate is minted for it just shows the fully qualified cloud SQL instance name.

Connecting with TLS/SSL certificates without the Cloud SQL proxy is definitely supported. 

I can't say for sure without more details, but it sounds like your driver is trying to fully-verify the certificate by making sure that the CN resolves to the same IP you are trying to correct with. I don't know which database engine you are using, but here is the postgres docs that explains this behavior :

> Once a chain of trust has been established, there are two ways for the client to validate the leaf certificate sent by the server. If the parameter sslmode is set to verify-ca, libpq will verify that the server is trustworthy by checking the certificate chain up to the root certificate stored on the client. If sslmode is set to verify-full, libpq will  also  verify that the server host name matches the name stored in the server certificate. The SSL connection will fail if the server certificate cannot be verified. verify-full is recommended in most security-sensitive environments.

If you make sure your driver is using `sslmode=required` or `sslmode=verify-ca`, you should be able to connect without any issues. Here's an example configuring a TCP connection using TLS.

Hope that helps.