I'm looking for can't find another way to edit finished custom scripts in menu - RENAME menu.
I know that it was not done in "Customize" mode but in normal mode. Hovered the mouse over the desired script and right click offered a context menu. This is not showing up for me now and I can't find any other way to edit the script.
That's a rename preset.
To edit it, first make sure "Use Simple Rename" is turned off. (It looks like it has been turned on, from the 2nd menu item in the menu in your screenshot.)
Then select a file and click the main Rename button. The list of presets will be on the left.