Who is it??

depends who you're facing but i'd say either AD shaco, AD trynd, or AD yorick. Udyr is also pretty good

There is no "best 1v1 champ." While a DPS can walk up to you and instagib, a well-built Shen who stacked armor could counter that easily.
If you built Last Whisper to counter tanks, someone who didn't build Last Whisper could probably kill you from sheer damage.

Some champions are designed to function well in 1v1 situations. Of these there are:
All assassins.
Udyr, Jax, Olaf, any AD carry
Essentially any DPS or sustained mage has a chance of winning a 1v1.

If you take the time to start comparing skillsets, I would say Tristana is one of the strongest in a 1v1 situation. Highest sustained DPS endgame (similar to Kog), if you get too close she ults/jumps away, and the healing reduction means any lifesteal is halved.
But even she can be countered with any bursty mage if it's glass cannon Trist.

um where is poppy

Akaliiiii

Poppy
Malz if u no QSS

Ad sion.

Crits for 1,000 with full build and has 100% life steal.

I'm pretty sure the pure variety of answers already here prove that the answer is 'no one'.

because there isnt any 1 "best" character. too many factors. early mid or late game? who is your opponent? whats their build? fighting ad sion and ap sion are completely different.

lvl 6 I believe used to be Nidalee, not sure now. lvl 18, Malzahar can combo any single target down if he has the AP, only counter would be QSS which alot of people don't build. But as said above, it really depends on their build and level, also 1v1 is fairly uncommon unless your playing a custom 1v1 game.