If all your users are domain users and all the computers are on the domain then a user should be able to log in physically with no issues. By default a domain user can log into any domain client machine.
If you are not on a domain then each computer would need to be configured to allow each user to log in. Since each computer is standalone you'd have to set up a per-machine accounts for each user. The fact that login names are the same across machines wouldn't matter in this case as each machine would have its own set of users.
If you need to allow users to remote desktop into domain computers then you would need to add the domain users to the list of remote access users allowed on the machines. You can do this via GPO as far as I know.