I have three NSMutableArray containing names that are added to the lists according to different criterieas.
Here are my arrays pseudocode:
NSMutableA
Have a look at this post.
In short: if you can use NSSet instead of NSArray, then it's trivial (NSMutableSet has intersectSet:).
intersectSet:
Otherwise, you can build an NSSet from your NSArray and go back to the above case.