What is the Greek name of violet?

The flower violet is ἴον /íon/ in Ancient Greek.

In Modern Greek, μενεξές /menekses/ < Turkish menekşe < Persian بنفشه ‎/banafše/ and βιολέτα < Italian violetta are more common.

Βιολέτα – Βικιπαίδεια

EDIT: the colour: in Ancient Greek ἰάνθινος “violet-flowered” or ἰόεις. Just as well, because ἰώδης is “rust-coloured = verdigris, green” (from the similar noun ἰός).

Modern Greek? You’ll occasionally find the derived terms μενεξί, βιολετί. But good old French μώβ (mauve) is the default for all variants of purple; and before it, I’m pretty sure it was λουλακί “indigo”.