The following situation allows for duplicate display names to exist:

Bob creates an account.
Bob decides to change to Bobby and edits their profile.
Bob's name change request is added to pending DisplayName changes to be approved by admin.
Meanwhile, Bob creates another account as Bobby.
No duplicates are found for Bobby and the Bobby account is made.
Admin finally approves Bob's change to Bobby.
Now there are two Bobby display names.

ALSO
The only check made for duplicate pending names is for a user's own change request. This means two people can submit the same display name request...and if the approving admin is not paying attention (not likely) they can approve the duplicate requests and it is allowed.

This appears to not be fixed in the 6.5 trial version on offer here, so I am reporting it.