I looked up Dr. W. PAPE’s Woerterbuch der griechischen Eigennamen. Dritte Auflage neu bearbeitet von Dr. Gustav Eduard BENSELER. Vierter Abdruck. Braunschweig, 1911, the big old Greek dictionary of proper names. It brings up the Byzantine authorities’ guesses, and they lean towards ‘wheat’. The Etymologicum Magnum says that the river Pyramus was so called διὰ τὸ πολὺ πυρὸν περιποιεῖν τοῖς ἐν τῇ Κιλικίᾳ οἰκοῦσιν “because it provides those who dwell in Cilicia with much wheat”. Eustathius of Thessalonica interprets it as a variant of πυράμινος ‘wheaten’.