Modifying a user is similar to a "move" operation. To modify a user, you need permission to remove the user from the current path or name, and put that user in the new path or name.
For example, if a user changes from one team in a company to another, you can change the user's path from /team_abc/ to /team_efg/. You need permission to remove the user from /team_abc/. You also need permission to put the user into /team_efg/. This means you need permission to call UpdateUser on both arn:aws:iam::123456789012:user/team_abc/* and arn:aws:iam::123456789012:user/team_efg/*.
To rename a user:
euare-usermod -u <user_name> --new-user-name <new_name>
euare-groupmod -u <user_name> -p <new_path>