A common question when reviewing the output of the #sh ip eigrp neighbors cmd is 'What on earth does 'H' stand for??'
Well, here it is......
H (handle): A number used internally by the Cisco IOS software to track a neighbor. It records the order in which the neighbors were learned.
So there you have it...still no clearer why the word Handle was used but at least you now know what it means :o)