You could try hashing, though its an inexact science. I would suggest using NSObject's isEqual: but I guess they won't be the same object, just two objects referencing the same file.
UImage doesn't keep a name of the file it was inited with. You need to do that part yourself. You could subclass UIImage and add a name property to it. Compare the names to find if they're the same.
Else, you can keep your own dictionary that uses the UIImage* as the key and the name as value. Or keep a couple mutable arrays with UIImages and names as the values.