So i have my Elytra and i have renamed it to a custom name. I have repaired it several times on an anvil and even added unbreaking III to it with a book.
From what i understand on the wiki, the cost should not increase once you renamed an item. This has happened with several Efficiency V pickaxes, shovels and axes and it is really starting to eat away at my diamond and enchanted book stash because i have to replace them when they get too expensive.
They are not supposed to do this and i have a set saved up for when mending books come to town.
I dont think the renaming of items to prevent the xp cost going up is a feature, its probably a bug on mc java which is fixed on pe.