Your predicate is fine.
I would double check the array and searchString:
NSArray *array = self.fetchedResultsController.fetchedObjects;
NSLog(@"array = %@",array);
NSLog(@"array count = %d",[array count]);
NSLog(@"searchString = %@",searchString);
NSPredicate *predicate = [NSPredicate
predicateWithFormat:@"name contains[c] %@", searchString];
NSArray *filteredArray = [array filteredArrayUsingPredicate:predicate];