It drives me crazy that I can't simply rename an action group. I have to go through the process of copying it, then naming the new copy to the name I desire, then delete the old action group.
And just try changing the name where you only want to change the case of some letters in the name. It takes two copies and two deletes.
You might consider adding a right-click menu to actions in the selection dialog, with 'Rename', 'Edit', 'Delete', 'Duplicate' and 'Insert'. Context menus are almost always easier (well, faster anyway) than using buttons. The insert would also give the ability to immediately place a new action at a certain point in the list instead of creating it new, then moving it into place.