Googling for "Math squiggle that looks like a cursive P" is not a very elegant or convenient way of learning new symbol names.
I wish every proof or equation came with a little table that gave the English pronunciation and some context for each symbol used.
It would make it a lot easier to look up tutorials & ask questions.
All of those you're of course expected to properly distinguish in handwriting.
I'm sure most of them have some sort of canonical name, but I'm usually tempted to read them with different intonations.
(Oh and of course each of those needs a separate Unicode character to preserve the "semantics". Which I imagine is thrilling edgy teenagers in YouTube comments and hackers looking for the next homograph attack)
"Fake-Handwritten R" is an extra fancy calligraphic version which is not hard to distinguish. The Fraktur R is a pain to write, but you can write an upright "Re" as an alternative.
The basic issue is that using single symbols for variables is very convenient (both more concise and less ambiguous than writing out full or abbreviated words when writing complicated mathematical expressions), but there are infinitely many possible variables and only a small set of symbols.
I grind hundreds of flashcards every night to learn Japanese and I can assure you that one thing we are not short of is symbols. Chinese characters use ~218 basic symbols which can be stacked and combined to form tens of thousands of characters. There are 350 symbols just for counting different kinds of things.
E.g. the two Rs we are talking about here both stand for the same word - Real. Except one is Real as in the Real numbers, and one Real as in the real part of a complex number.
If you go with a random symbol, you're putting a different kind of cognitive overhead because you have to map a random symbol you never saw before to a specific concept. Here you just have to distinguish font, and even that is often not necessary, because you often are dealing with a branch of maths that only uses one of the meanings.