The bug

The experience level cost to rename an item in an anvil scales with the enchantments and/or repairs on an item. More specifically, the cost to rename an item follows the function 2^n where n is the number of enchantments or repairs done to the item.

This results in weapons and tools having their renaming costs increasing as more repairs and enchantments are added to it. Eventually this cost will top out at 39 levels just to rename a single item.

Renaming an item costs only 1 level when you rename it and also enchant/repair it. Therefore, it is a bug that only renaming the item after enchanting/repairing it costs more than 1 level.

How to reproduce

1. Enchant an item in an anvil
2. Put the item in the anvil and give it a new name
3. Observe that the renaming cost is now greater than 1 experience level and is based upon the number of enchantments put upon the item

This effectively punishes the player for obtaining good enchantments, then renaming the item later. The rename should always cost 1 level regardless of whether a enchantment (or repair) has been added or not.

Image explanations

The first image shows that renaming an unenchanted item costs 1 level.
The second images shows the cost of the sword when you only enchant it (21 levels)
The third images shows the cost of the Sword when adding the enchantment(21 levels) and the enchantment (1 level) for a total of 22 levels of cost.
The fourth images shows the bug. If you rename an item with enchantments already on it while not enchanting/repairing the item at the same time, you will be charged more levels (in this case 16) to rename the item instead of just 1 level like the previous images.