It has now become clear that I am not interested in using the integer figure handle as a handle, but as an identifier with which I can organize figures and find a figure window (or file) in a larger number quickly and unambiguously. In principle, I would like to have a kind of number property that exists independently of the handle.
The tag property would be just as suitable if it could appear in the window name instead of the number (à la f.TagTitle = “on”).
So far, I have used the figure name only to describe the content of the figure. With a little bit of adaptation, I can also prefix it with an identifier. I therefore accept Ayush Modi's answer, but thank everyone for their contributions and would be happy to receive further suggestions.
I still wish there was a native way to duplicate/clone a figure, but that's another topic.