Your domain is being renamed, or your server is moving to another domain?
If your domain is being renamed (not that I would recommend renaming a domain), the SID's should still be ok and everything should be fine.
If you are moving your server to another domain, if you are using Windows Integrated security, you will either need a trust relationship to the old domain so the users can be authenticated, or you will have to drop the old users and add the users from the new domain. This is also the case with users and groups at the Windows Server level.