Can't find the reference to the most common Ukrainian surnames but think the most common ones have "professional" background.
And, in my opinion the most common are:
Shevchenko, Kovalenko, Gonchar, Petrenko, Tymoshenko, Shevchuk, Kovalchuk, Melnik, Melnichenko
See, the Slavic variations of the "(Black)smith" are always among the most common: Kuznetsov, Kovalev, Kovalchuk, Kovalenko, Koval', Kovačević, Kovačič, Kovač, Kowalski, Kowalczyk, Kowalewski, Kowacz, Kovačević etc.
Ukrainian suffix – enko (somebody's son) has probably the same origin as German -ing, -ink transformed in Easter Russian dialects into -yak, -yag because they when borrowed from Western Slavic languages lost nasality.
Varing – Varyag
Koning – Konyag-Konyazi-Konyazhe- Knyaz'