I mentioned the login thing by way of illustrating the persistence of the oldnames.

I don't want logins for individuals at all; they should have access by way of their group memberships.

SQL Server is not able to resolve their newnames at all, and thus won't let them login.

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Are you sure a new sid is created on a rename? From MS:

• Because it retains its security identifier (SID), a renamed user account retains all its other properties, such as its description, password, group memberships, user environment profile, account information, and any assigned permissions and rights.

I'm wondering if the problem is the newname AD accounts that were created by copying the oldname accounts. That would generate a new sid. More from MS:

...Microsoft provides the ClonePrincipal API. When you create a new account, the API automatically adds the old account’s SID to the SID History attribute of the new account. The security logic that creates the user's access token then adds the content of the SID History attribute to the token. As a result, when the user logs on to the new infrastructure by using his or her new account, the access token will refer to the new SID and to the old SID. The user can then seamlessly access resources secured with the old SID hosted in the old infrastructure.

And then when I delete the cloned newname account, and rename the oldname account, might that be where the confusion creeps in? But that doesn't completely explain why I only have problems on one server...

If I could find a way to see the sidhisory table, I could rule this in/out.