Where does “Ἀριστόμαχος” come from?

Ἀριστόμαχος (Ancient Greek) comes from Ancient Greek ἄριστος, from Proto-Indo-European h₂éristos, from Proto-Indo-European h₂er- — to fit, to fix, to put together.

Ancestry of “Ἀριστόμαχος”, step by step

Ἀριστόμαχος traces back through two separate lines of ancestry.

via Ancient Greek ἄριστος

Step	Language	Word	Meaning
1	Ancient Greek	ἄριστος	best (in multivarious contexts)
2	Proto-Indo-European	h₂éristos	fittest, most fitting, most suitable
3	Proto-Indo-European	h₂er-	to fit, to fix, to put together

via Ancient Greek μάχη

Step	Language	Word	Meaning
1	Ancient Greek	μάχη	battle, combat; quarrel, strife, dispute;...
2	Ancient Greek	μάχομαι	I make war, fight, battle; I quarrel, wrangle,...
3	Proto-Indo-European	maHgʰ-	to fight

Every word from Proto-Indo-European h₂er- →Every word from Proto-Indo-European h₂éristos →Every word from Ancient Greek ἄριστος →