I am trying to filter out a NSArray of NSDictionaries. With my below example, I want dict1, dict2 & dict4 grouped in one array, dict3 & dict5 grouped in second array
If the desired output is an array of arrays, you can get there by building a dictionary keyed by the name attribute in the orig dictionaries:
- (NSArray *)collateByName:(NSArray *)original {
    NSMutableDictionary *collate  = [NSMutableDictionary dictionary];
    for (NSDictionary *d in original) {
        NSString *newKey = d[@"Name"];
        NSMutableArray *newValue = collate[newKey];
        if (!newValue) {
            newValue = [NSMutableArray array];
            collate[newKey] = newValue;
        }
        [newValue addObject:d];
    }
    return [collate allValues];
}
It's a little verbose, but clear, I think. If you want to decide the attribute to distinguish with programmatically, pass in another param called attribute and replace the literal @"Name" with it.
It's a little hard to tell if what you want is three different arrays where each one only contains entries with a specific Name value (as your first paragraph suggests) or if you want a single array where the entries are sorted by Name (as your second paragraph suggests). Regardless,
To sort orig by the value of the Name field:
NSArray *sortedByName = [orig sortedArrayUsingDescriptors:@[[NSSortDescriptor sortDescriptorWithKey:@"Name" ascending:YES]]];
To get a new array by selecting only entries with a specific value for Name:
NSArray *t1Only = [orig filteredArrayUsingPredicate:[NSPredicate predicateWithFormat:@"Name = %@", @"T1"]];