Where does “Ἀνδρομάχη” come from?

Ἀνδρομάχη (Ancient Greek) comes from Ancient Greek μάχη, from Ancient Greek μάχομαι, from Proto-Indo-European maHgʰ- — to fight.

Ancestry of “Ἀνδρομάχη”, step by step

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

Ἀνδρομάχη — Etymology, Origin & Word History | Etymology Explorer