^{Update by Mega_Spud:}
Summary:
Renaming an item using an anvil increases the prior work penalty, it should not.  It should only add a single level, plus any prior penalty.
 
Wiki:
Renaming always costs a single level, in addition to any Prior Work penalty. Renaming will not increase the prior work penalty.

Repro Steps:

1. Obtain sufficient XP
2. Switch to Survival
3. Rename a new sword in an anvil
4. Notice the XP cost
5. Rename it several more times, and notice the exponential increase in cost

Observed Results:
The costs doubles each time it's renamed. In Survival, the item will become 'too expensive'  to upgrade, rename, or repair.

Expected Results:
Renaming should only cost one level each time, and should not add to the prior work penalty.

Screenshots/Videos attached: Yes (YouTube link)

Notes:

Original Description:

According to wiki page "Anvil mechanics", renaming items should NOT increase the prior work penalty(Java Edition 1.13.1 works well).

Affects Platforms: iOS, WIN10

Video Link: https://youtu.be/eTEXjjQltlI