Renaming Nintex configuration database during migration

Is it supported and if so, how do you properly rename a configuration database during a migration between one farm to the next (eg. when upgrading SharePoint)?

We’ve tried to attach a config database that has been renamed to match the environment it’s now in, but the operation fails with an error stating it can’t find the database with the old name. We’ve run the _PrepareForNewEnvironment stored procedure before attempting to attach the database.