To my knowledge, scriptrunner plugin won't update the username values in the single/multi user picker customfield. You have to update the database for these customfield with desired username and then you can go ahead with renaming the user.
NOTE: Update the database for the customfield values before renaming the user using the above plugin. Remember to take a backup and shut down the JIRA instance while updating the table. Once verified at the database level, restart jira and reindex it and check if the changes are reflected.
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