I'm on Purpur-635 for 1.16.1. I'm using ImageOnMap v4.0
Here is a video on how to reproduce the issue:
https://imgur.com/a/RgX2eV3

Hi and thanks for this report! I think I see what the cause can be, but do you have an error, an exception, or something, in your console, either when opening or closing the sign, or when you interact with an inventory after that?

I digged, it seems to be caused by the prompt (sign). after renaming you should have to leave 2 inventories (the map selection and the map part selection) but you only have to leave the map part selection. The plugin then thinks that you are still in the map selection one and replace item in inventory.

Fixed by #137 will be added in next update, thanks for the report :)