Matthew m. Hebrew מַתִּתְיָהוּ 'gift of the Lord', Hellenicized as first as Ματταθίας and then shortened to Ματθαῖος.
The name of one of the twelve apostles, one of the four evangelists, and a 15th C king of Hungary and Bohemia. Wycliffite Bible (1395): Matheu.
By the end of the Middle Ages, Matthew and Matthias were considered distinct names, despite their shared origin.
Mahé is a typical western French spelling, while Mahieu is more typical of Normandy and Picardy.