Updated June 9, 2019 Share: Family name origins & meanings Polish, Czech, and Slovak (Koník) : from koník ‘pony’ (a diminutive of Polish koń, Czech kůň ‘horse’), a nickname for someone thought to resemble a pony in some way, for example in short stature or docile temperament.Jewish (Ashkenazic) : variant of Koenig.Dutch : variant of Koning.