What is the version of vCenter server?
Below KBs are for changing vCenter hostname, but it should help to change vCenter domain name.
Make sure new vCenter dns record works fine.
You may need to replace SSL certificates to match the new fqdn
Go to SSO and update identity sources and add new AD for AD user permissions if you use it.
See these KB -
It´s vCenter Server 6.
well, it looks you cannot change the vCenter 6 Hostname or fqdn.
See this, you may end up with errors. So its good to deploy new vCenter and add host in new vCenter.
If you are running vCenter in VM, you can take snapshot and try to change domain name using previous steps and revert back to snapshot if you get errors.
Or the safe option is to deploy new vCenter and add host to new vC.