Anyone using symbols to mark move typing?

No because a letter (or two at most) would inform me of the specific move on Pokemon with 2 moves of the same type.

I just use letters. If the letters are ambiguous (for example Gyarados can have both dark and dragon moves), I'll use an extra lower-case letter (e.g. "Da" or "Dr").

I do use some symbols, this ⁂ for poison and this ¥ for steel, because it's easily available on my keyboard. Maybe they don't make much sense, but I'm used to them.
I also have one for fire, which I grabbed from the standards of the app Calcy IV, but I couldn't copy it here, it only appeared as ":hotsprings:". It appears if I try to write this on WhatsApp Web or Telegram Web.
I'm still looking for a symbol for flying, though.

Some do, some don’t . I personally don’t because I really only use about 40 different Pokémon of various species since day one have their movesets memorized from thousands of battles.

You could use: fire - 火， water - 水， ice - 冰， normal - 普， ground - 土， rock - 石， flying - 飞， dragon - 龙， electric - 电， steel - 铁， fighting - 斗， poison - 毒， fairy - 灵， ghost - 魂， grass - 草， bug - 虫， dark - 黑， psychic - 心

There is a character limit on pokemons' names, but the count is for uni-code characters. Chinese characters are a bit more compact way of expressing meaning, than Latin characters.

I just use:
#Fire
$Steel
£Air
€Water
¤Bug
@Psycho
%Fight
●Dark
_Ground
^Stone
♧Grass
♡Fairy
☆Ice
◇Dragon
~Electric
&Ghost
○Normal
!Poisen
Works fine for me.

Nope i dont use symbols. I have all my pokemons cp And moveset memorized. I use these pokemons almost everyday it's hard not to know the exact iv stat, moveset, cp, position of Pokemon order when scrolling from cp and stuff. I even have hp memorized for most of my pokemons too. If I have same Pokemon with 100iv I still know. I'm pretty sure I got at least my top 24 or 36 Pokemon from highest cp memorized in order, cp, moveset, where I caught it or if I hatched it, and exact iv of that Pokemon from memory.

No. I give all my Pokemon unique names and I know exactly what they're packing because I know each and every one of them like a real trainer should.

Post-evolve IV information is useless because if I decided to evolve and power them up, then those criteria have already been vetted and deemed acceptable.

Nope, I just abbreviate the name of the move. For example: WF/HP is a Waterfall/Hydro Pump Gyarados. Symbols tend to take longer for me to interpret, and they don't help me if a Pokemon has multiple moves of the same type.

That being said, I know several people in our local raid Discord who use symbols for move typing.

I've found the symbols that work depend on how the operating system youre using handles the symbols. On Android 7 I am using:

Normal ⵙ
Grass ⸙
Water ꧞
Fire ♨
Ice ❄️
Electric ϟ
Psychic ໑
Ghost ᗣ
Flying ༄
Fighting ꢳ
Rock ☖
Ground ᨏ
Bug ꣔
Poison ⚠
Dragon 中
Dark ◐
Steel ۞
Fairy ♡

PS. If you want to add symbols I suggest adding them as shortcuts to your keyboard so you easily type them in when renaming mons.
Eg. dk = ◐