NSSet *set = //your set.
NSArray *nameIndexes = //the array of names for sorting.
NSArray *result = [[set allObjects] sortedArrayUsingComparator:^NSComparisonResult(MyObject *obj1, MyObject *obj2) {
int index1 = [nameIndexes indexOfObject:obj1.name];
int index2 = [nameIndexes indexOfObject:obj2.name];
return [[NSNumber numberWithInt:index1] compare:[NSNumber numberWithInt:index2]];
}];
Not 100% certain what you are asking but this will sort take the set of names and turn it into a sorted array sorted based on the index of the names in a second array.
After edit
Edit... ok, so your edit completely changed the question. Anyway, from the edit you can just do...
NSArray *result = [[set allObjects] sortedArrayUsingDescriptors:[NSArray arrayWithObject:[NSSortDescriptor sortDescriptorWithKey:"name" ascending:YES]]];
This will take the set and return a sorted array sorted by the name property of the objects in alphabetical order.