Service ID for SQLServer will need changed on the Configuration panel...
UserIDs: Need to give that service ID on the new Domain 'sa' rights...
All users using their domain ID within SQL Server will need recreated on the new domain within sql server....
If it is a clustered SQL Server there are many more steps. You don't say it is clustered so I am guessing it isnt
If you can do cleanup, the new service ID should NOT be a Windows or Domain admin.
If you run into file by file NTFS security issues, from the command line
icacls * /reset /t
is useful - it'll set an entire (SQL Server) subdirectory tree to the same permissions as the directory you're in, if you get into a problem.
Don't forget to set your SPN's again, and make sure the new domain service account is trusted for Kerberos delegation.
Check to be sure @@SERVERNAME and SERVEROPTION('servername') report the same name after you're done.
If you've got "Force [connection] encryption on" you'll need to generate and sign a new SSL cert because the FQDN changes, and you will of course need to grant Read permission on the private key to the new service login.