There are only 36.

https://backpack.tf/profiles/76561198128213644?time=1484006400 - Sort by time, the 36 keys group together

http://www.tf2outpost.com/trade/28653089 - His B/O was also 36

I'll try to explain more carefully how item ID#s work. So every time an item is traded, painted, described, returned to your inventory from SCM, etc, it is given a new ID# by Steam. This process happens very quickly, with hundreds of ID#s being assigned simultaneously at all times. When Mr Creepy acquires the Billycock, the ID# that Steam assigned to it was 5428494844 (visible in the item history). When TheRealSlimMuffin acquires the 36 keys on the same day, they are assigned ID#s ranging from 5428494858 at the lowest to 5428495119 at the highest. The close proximity of these numbers, with the Billycock being only 16 numbers apart from the nearest key, demonstrates that these items were traded for one another. Steam processes these numbers so quickly that if they were acquired even a few minutes apart, there would be a much more appreciable difference. Generally speaking though, I look for the first 6 digits to match.

In this case, the names not matching really does not matter at all. Names only update when the backpack is scanned on backpack.tf, so if items are acquired and traded before this happens they will never show up as having been owned by that person in their item history on this site. However, names and ID#s are still both worth paying attention to. There are various scenarios where the names will match but the ID#s won't, or the ID#s will match but the names won't. Always check both, but you only need one or the other to confirm a trade.