Exactly what are you trying to accomplish with this data structure?
Maybe an NSSet of NSArrays is a poor choice for what you want to accomplish? Beginners often make poor choices of data structures, which turns into a "How do I do X with the Y data structure?" question as difficulties arise. The real question should be "What data structure(s) can I use to accomplish goal Z?" Without knowing the goal, and all the things expected from the data structure, it's hard to answer either question well.
If I had a bunch of NSArrays, where each one's first item was treated as a name, and I had to retrieve an NSArray by name, I'd use an NSDictionary. The key would be the name to retrieve by (i.e. first item in NSArray), and the value would be the NSArray itself. This assumes names are unique, which is somewhat implied by the use of NSSet and the description provided so far. I might not use an NSArray for storing the items; it depends on what I was going to do with the items therein.