Just a (very) wild guess, because you are talking about .txt files.
When you open a .txt file in Notepad and click on the cogwheel (upper right of the menu) a windows will open, called "Settings". In the line "Opening files" (or similar, my computer is in French) in that window, you should have two options: "open in a new window" or "open in a new tab".
Could it be that another tab of the same file is still open, when you try to change the file name ?
If the option is set to "open in a new tab", change it to "open in a new window". It's a new - in my opinion useless - feature in Notepad (since a recent update), that it always creates a new tab when you open Notepad, leaving the old tabs open ! You end up having more and more open tabs, whenever you open Noteapd.