Your F2 hotkey is running the Rename command twice. The first time it forces the dialog to appear and shows a preset which renames things but does not move them.
When you click Apply in the dialog, it only Applies what is in the dialog. If what is in the dialog does not move anything then clicking Apply in the dialog will not move anything.
The second Rename command is the one which actually moves things, as a second and separate step, and that one is set not to show the dialog. (If you add the ADVANCED argument to the second Rename, like it is there on the first one, then it would show the dialog. But you'd then go through the dialog twice when you pushed F2, which probably isn't what you want.)
You could combine both actions into one action/preset which could then be run from a single command (or loaded from within the dialog itself). Then clicking Apply in the dialog would do both steps at once.
Combining them into a single preset would involve either working out a regex that does both things at once, or using a script to apply one regex after the other.
Many thanks for your explanation Leo. Appreciate your taking the time to make it understandable, even for me..
Whilst I understand it, I am afraid combining both actions into a script or new preset, well, that is, let say 'a bridge too far' for me, at present.
Anyway, thanks again.