The following mobs despawn even when named:
bat
blaze
cave spider
creeper
dolphin
drowned
enderman
endermite
evoker
ghast
guardian
hoglin
husk
illusioner
magma cube
ocelot
phantom
piglin
piglin brute
pillager
ravager
silverfish
skeleton
slime
spider
squid
stray
vex
vindicator
witch
wither skeleton
zoglin
zombie
zombie villager
zombified piglin

These mobs stick around when named:
bee
cat
chicken
cod
cow
donkey
fox
iron Golem
snow Golem
horse
llama
mule
mooshroom
panda
parrot
pig
polar Bear
pufferfish
rabbit
cod
sheep
shulker
skeleton Horse
strider
tropical Fish
turtle
villager
wolf
zombie Horse