Re-renaming Costs Exponential Levels

I heard that renaming now only costs one level. However, I found that when you rename an already renamed object, the cost of levels doubles. First it costs 1, then 2, but then can be repeated to get to 4 and 8 and 16 and 32. Enchanting the item at the same time with enchanted books makes it a bit more confusing.
(Personally, I think that the fact that Minecraft remembers how many times an object is renamed is surprising and neat, but in this case annoying.)