How do I change the name of master / parent role keeping the name of derived/child role same? I would like to keep the name of derived /child role same and also the profile associated with the child roles.

First copy the master role using PFCG to a role with new name you wish to have. Then you have to generate the role. Now open each derived role and delete the menu. Once the menus are removed it will let you put new inheritance. You can put the name of the new master role you created. This will help you keep the same derived role name and also the same profile name. Once the new roles are done you can transport it. The transport automatically includes the Parent roles.