In running a workflow that renames the target 'Microsoft SQL' or 'MySQL' object says successful, but does not actually commit the change. Subsequent workflow runs find the original object name and attempts to update the object again.
This happens when using the samAccountName as an identity object. 'Microsoft SQL' or 'MySQL' workflows are different than ActiveDirectory to ActiveDirectory workflows in that the mappings have other fields that are also used in maintaining the mapping pair such as object 'GIUD'. 'Microsoft SQL' or 'MySQL' table objects do not contain the same 'GUID's' and therefore do not commit the change.
Create or use another field for the identity. This is most commonly a field such as 'employeeID'. It is also possible to create a field in both locations, thought that is not as effecient as using an existing field with values in them that are unique already. Please see attached screenshot of where to specify the Identity value. This can be set when configuring the 'Microsoft SQL' or 'MySQL' Connections in both the 'Connection Creation Wizard', or in the 'Connection Properties' page.
See attached screenshots: 'Identity Wizard' and 'Identity Console'