How do you guys name your Pokemon?

I do nothing too complicated.
I put an abbreviation of the moveset at the end of the name. This way I know what I am selecting when I choose my team, and in combat.
Vapes just get their charge move named (At Wp Hp)

eg
Exegg CSoB
Tyranitar BC
Snorlax ZHb
Alakazam CFs

Simple but effective

I name them by IVs. I already know they have the move sets I need so its a simple symbol by their name

♚ perfect IVS
♤ 15 attack
♡ 15 stamina
♢ 15 defense

I have two different naming conventions.
For mons to be evolved:
if they are future defenders, I'll include the max cp in their name.
if they are future attackers, I don't really care about IVs, I just weed out the lowest ones based on just reading the appraisal. I'll evolve but not power up.

For my evolved mons they are name by
type quick-attack charge-attack

this way if I sort by A-Z, the mons get sorted by type and moveset.

I'll only favorite the best attacking movesets and if the CP is below 2500.
I sort by favorite to pick my prestige team
I sort by CP to pick my attacking teams.

(I'm sure there are better ways, but so far this is OK)

Note: I don't include IVs in the name, to me it is useless information.

This is how I have @ for offence and an emoji for defence also at the end I have the ivs

To me what is important is having them organized for prestiging and attacking.

If I'm adding a defender, I sort by CP. If I'm looking at my overall Mons, I usually sort by #

So I name my attackers and prestigers with a symbol In front, like you suggested.

Attacker is $ plus the type.

So my Hydro pump Vaporeons are "$water"

I don't need the IV. I have already identified them as my best Vaporeon, with the best attacking moveset, so why is IV important in the name?

I have a 2nd tier of prestigers, and they get a "@" in front.

So, for example, I have lower level Vaporeons that are named "@water"

It works really well.

if you have 81iv eevee, name it "eevee 81"

lets say you have 91iv dragonite, 100iv snorlax and 94iv snorlax

91iv dragonite with dragon tail and hurricane, you would name it "A/D dt/h 91".
A/D= Attack/Defense
dt/h= dragon tail/hurricane
91= 91IV

100iv snorlax with lick and hyper beam, you would name it "Att L/hb*"
Att= Attack
L/hb= Lick/Hyper beam
*= 100iv

94iv snorlax with zen headbutt and hyper beam, you would name it "Def zh/hb 94".
Def= defense
zh/hb= zen headbutt/hyper beam
94= 94iv

For pokemon with usable movesets, I include a 1-3 character abbreviation to identify their moveset at the end of their name.

For my prestigers, I put the first three digits of their CP (including 0 if less than 1000) first in their name so I can sort by name and get all my prestigers in ascending order. (Don't need the full CP. Sorting within 10pts is close enough.) Then if I only want to select a few prestigers, I can quickly select lower mons for the remaining slots.

I have room for a 4-6 character abbreviation of the mon's name with 2 digits for their IV percentage (* if 100 to save space)

Before I run a pokemon through PokeGenie, I put an abbreviation for its appraisal so it is there on the screenshot later.
Overall: 0,5,6,8
Highest IV: HAD
Value: 0,8,13,15
For example:
6D13
8AD15
6H8

Also, for defenders with a "Battles Won" on them, I add a little crown ^ after their IV number.

I only bother naming mons in the highest appraisal tier (i.e., 82%+), the rest are usually getting transferred. I don't need the name anywhere in there because I can see the damn sprite, but I definitely want to know it's overall IV percentage and which attacks it has (extremely useful when attacking / prestiging gyms on the quick). So for my pride-and-joy Venusaur, I go with "100% RL/SoB", and that's usually sufficient. My Rhydon's "89% MS/SE" and my Gyarados is "91% DT/HP".

Eev z 80aTR

Tells me it's an Eevee/Vaporeon in a gym at Zigabalis' {local restaurant} IV80 best attribute attack good for killing Tyranitar and Rhyhorn.

Actions
Name
IV (% or ranked A/D/S)
HP (after %)
Moveset (after A/D/S)
HP (after moveset if needed)
If for defense, add a letter "g".
The type to use against
Example:
*Shu.32vrock
Gyara.91%122
|Pinsir

Something that relates to the name of the mon and or their moves followed by the percentage of IVs. I use ! For 100%

Example: Bombpalm! (Who's that pokemon?)

I name them for the A-Z sort to make my attack team easy to find. A leading number: 0 - usual attack team for other team gyms, 10 - usual attack team for prestiging, 1 - mon I might want to switch into the prestiger team, 2 for potential prestigers for gyms that are full of low CP mons. Species name. Something to help me to identify the specific mon. For example, sb to let me know this is the venusaur with solar beam. I sort by favorites to find mon to switch into my primary attack team, and my defenders.

stats in hex
like DFF - 13-15-15
then moveset
like DtO
for Dragontail - Outrage

I give my favourite and best 'mons names in Chinese (since I'm learning it). I will either make a play on the sounds of the name (for example my Gengar is 更高性能 [geng-gao-shining- nung] which means "high performance" (because he's 100% with ideal moves). Or I name them something memorable, fun or silly 蛋菠蘿通靈蛋 "egg-pineapple-psychic-egg".
The rest I just name them by iv percentage and abbreviate their attack moves.

You're all so meh and bleh. Monsters that I'm definitely keeping have normal names. Many of the cute ones are named after food, e.g. Wigglytuff is a pink balloon so it's named Bubblegum. With some symbol before its name because it's a prestiger, to make it easier to find. If I don't know whether I'm keeping that prestiger it's just # because it's sorted the first. Attackers and defenders are sorted by CP and everyone is faved to prevent accidental transfer.

I named them like this:
IV Stat Moves
Ex.
Arcanine 98 IV 15 15 14 Fire Fang + Fire Blast
98 554 FFFB

Exeggutor 98 IV 14 15 15 Confusion + Solar Beam
98 455 CSoB

Funny enough only the ones I don't use need extra info like big O for A attack moveset or small o for B attack move set (from offence).
@ for suicide squad, above 700(2-3 rezolve a 3k snorlax prestige), up to 1900 piloswine without double ice.
& for my around 15 top prestigers, 1400-1500 range that I use to prestige non blissey towers for 6k prestige.
Then useless effort to put 0-7 as the name for prestigers with A and an extra o for B movesets I never used, based on thier CP ofcourse(0 bellow 1050, 1 bellow 1150 and so on).
Top attackers and defended I know them all just based on CP and expect this is similar for most that build their tram the hard way. They usually get names from a debate with my 9 year old.
Blissey prestigers have either dedicated names(Arcanines) or are just there, in 2100-2400 range, in 3-4th screen.
WP Vapes get a D at the end, because they just defend(remains from pre gen 2 times).

I use practical names for things I plan to use once for prestiging, then transfer them. Like if I evolve a couple dozen Furrets, I'll add "d/n" onto the name for any with dark quick attack and normal charge attack, then so on for each combination.

For any I plan to use repeatedly, I just give them random names when I feel like it. Such as, the one Snorlax I've bothered to power up at all is named Bob, my main Espeon is Purple Cat, my best Flareon is Garbanzo, and my Ursaring that's the only decent Pokemon I have with dual fighting attacks is named Shin Kicker. And then I started naming all my Jolteons permutations of Sparky, so I've got Snarky, Sporky, Spazzy, Sharky, Spanky, etc. Kinda running out of names like that, though.

Anyway, yeah, not much of a system, but it is usually good enough to know which is which, when it's one I care about distinguishing.

I put info in the name that isn't knowable from looking at the mon list (i.e., not species or mon type).

My first three characters indicate charge move type, CP range, and quick move type (if different). When I sort alphabetically, I get all mon with grass type charge moves grouped roughly in order of CP, then all mon with fighting charge moves roughly ordered by CP, then the next type, and so on. This system is good for me because when I prestige I like to choose mons quickly and get the best type advantage matchups.

After these characters, I put gender, IV, GP move ratings, and occasionally some miscellany at the end.

I feel that symbols get too complicated. And don't think I need the Pokémons name - I know most of them, and it doesn't help me battle, and I don't sort them that way.

So I use:
IV
Game press move ratings
pogomoves.com move ratings.

You near all guys use ivs and attacks in names but names of my pokes are normal- ussually names of my friends

i just give them diferent names like jhon of the rain or tom of fire and just remember what he can do and how strong he is and most if all i keep only strong ones;)

Attackers: only puns

Prestigers: moveset abbreviations​

1. NameIVquickinitialsCHARGEINITIALS

e.g.Jolteon89tsB, Ursari98mcHB, Dragoni96swH, Golem96msAP, Ursarin84cPR

I will just shorten the name if I run out of characters. I try to avoid adding irrelevant moves (water gun on Vaporeon). For the moves that share initials, I changed convention a bit (Thunder = T, Thunderbolt = B, Solar Beam = So, Sludge Bomb = Sl).

I use this system for most of my keepers.

2. For defenders, I replace the moves with location of the gym in which they reside. Otherwise, I'd never remember them all. I know efficiently where to return, which gyms hold, etc. For gyms I frequent, I make them specific (e.g. Lak for the Lake Apartments). For gyms I just passed in my travels, I just name them after the City (e.g. Ctrv for Centerville).
3. All cannon fodder (aka the suicide squad) get the name of 1.
4. All evolves for xp get the name zz (so they list after zubat).

I sort by CP if I want to check my defenders.
I sort by name (putting the 1s at top) to prestige with faint-then-transfer mons.
I will sort by CP and scroll down to half the lowest if I need more than cannon fodder.. I usually have enough suicide squad members to prestige. This greatly saves resources. I usually only dodge charge moves.
I also sort by name if I do a mass evolve (just scroll to the bottom for zz).
I sort by # when I do my mon database maintenance.