Hello Gordon
As Adam says, change the user id is not a good practice, in fact, this case is evidence that security standards have not been applied or used in the customer site, it is often by legacy applications that make this defect is inherited
The best for me would be not rename the user id and apply standards to rearrange applications and / or internal customer processes
If the customer need to change the user id in "Identity Manager" they will surely want to do it also at the endpoint, keep that in mind because is additional work and in some cases it is possible and not others, it depends of the type of connector / application because some do not allow rename account on the endpoint and you should recreate the account on it.
In the current version of IM, this functionality doesnt exist(I think), maybe because goes against the best practice. I had a customer implementation with an old IM version and they were requesting the same, in that moment was possible using a rename because the User Store was the same Provisioning Directory, so we used a "legacy package" published as JIAM API which is in deprecate mode( https://support.ca.com/phpdocs/7/5655/5655_Deprecation_Policy.pdf ) and this give us the possibility to rename the Global User and maintain associated accounts, but keep in mind that you will need rename too the user id in you User Store, because newer versions require that repositories (User Store and Provisioning Directory) be separated.
According to the CA Technologies documentation they should move API JIAM to TEWS APIs, but I still have not seen this update. I opened a ticket for improvement three years ago but has not been materialized
Good luck
Efren