The correct IUPAC name of K _ 2 MnO _ 4 is:

The structure of the IUPAC name is 

name of cationic part + Name of anionic part.

Metal present in the anionic complex, so 'ate', must be added at the end of the metal name. 

Oxidation state of $Mn$

$Mn + 4\left(- 2\right) = - 2 = + 6$

The structure of anionic complex name is

ligand names + metal name(oxidation state)

${K}_{2}{MnO}_{4}$

$2 + x – 8 = 0$

$⇒ x = + 6$

Oxidation state of $Mn = + 6$

IUPAC Name is:

Potassium tetraoxidomanganate \left(VI\right)$