You should understand the implications of changing a group's path or name. For more information, see Renaming Users and Groups in the IAM User Guide.
To change an IAM group name the requester must have appropriate permissions on both the source object and the target object. For example, to change "Managers" to "MGRs", the entity making the request must have permission on both "Managers" and "MGRs", or must have permission on all (*). For more information about permissions, see Permissions and Policies.