Depending on how large the rename is, the database can be inconsistent during the process:
- Update user.user_name, officially changing the name of the user locally
- Update logging, image, and other tables. This can take some time depending on how active the user is
- Update centralauth's localnames.ln_name row, which is what Special:CentralAuth uses.
If 2 takes a long time and 3 hasn't happened yet, it's likely that Special:CentralAuth will throw an exception for the old name.