So why does Tahm Kench get a last name. Plot twist he's the only one who cares to share
Ok so when riot released Tahm Kench like many others I realized he had two names. This led me to wonder why other champions don't after much thought I have an answer for each and every champion ... yes I have too much free time ... yes I know I should spend it climbing elo.
Moving on first is
he's easy Darkin's don't have last names.
she's a fox in more ways then one, so no need for more then a first name.
are all ninjas and any good ninja doesn't need to share a last name. Naruto doesn't count for reasons.
His last name is tribe's name.
actually has two reasons why he doesn't have one. one he probably forgot it, and two he's a yordle; I'll explain more later.
All the freljord champions
are known by their tribes and by there ancestry so no last names required.
her parents don't believe in that stuff ... I mean there parenting style leaves a lot to be desired.
So actually in shurima the custom is to show relation by sharing the last syllable, so if sivir has kids their names will end in ir. 
MYSTICAL BEINGS HAVE NO USE FOR NAMES.
are all robots so no last names yes I know ori does but it's creepy so i'm going to ignore it.

i'm going to file them under demon and move on.
doesn't like using her family name she got where she is on her own.
all have proud last names that carry weight and they use it.
fun fact we call them by their last names.
THE VOID HAS NO USE FOR LAST NAMES.
Ok so all the yordles
don't have last names because they don't need ones in bandle city. it isn't their custom
putting him by himself to prove that in bandle city everyone is family or else bad things happen.
are brothers and orphans.
their tribe doesn't believe in last names.
Mundo forgot mundo's name if you have problem with that cleaver.
not on good terms with his parents.
THERE ARE NO LAST NAMES IN DEATH. yes yorick has one but it literally means death.
explorers don't need last names.

plants animals and minerals do not require last names.
those are their pirate names like blackbeard.
he doesn't need much more then graves does he.

they kinda don't use them you are known by your style not your family
doesn't feel worthy of it.
orphan.
mystery
heroes only need one
probably to crazy to remember
he's probably shurimain so din.
sisters none given.
he lost the only person he wanted to share that name with. He needs only vengeance now.
let's go with har.
chose new names when the ascended.
forgot it. doesn't need it.
jaguar since she was raised by them.
doesn't need a fancy last name to be awesome.
to be fair we are lucky to know his first name plus all the greats go by only one name.
names don't matter to someone in exile or to the noxian military.
frankly he's so broken a last name would be op.
... I feel like I should call him a demon but like the joker you only really need one name.
dragons don't have last names.
family is famous but he could care less about them.
when you defy death ... or die that many times you don't need a last name.
semi all powerful being really doesn't have time for a last name.
orphan ... wow LOL has a lot of those
.
so fabulous he only needs one.
that's not even his real name.
spirit shamans need only one name.
same goes for villians.
it's actually Dracul.
lost his right to one.
rath
ZAC is an acronym anymore would be greedy.
gave it up as atonement.