Matthew m. Hebrew מַתִּתְיָהוּ 'gift of the Lord', Hellenicized 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.
The English diminutive Mate is witnessed in 1379 in the relational byname Matesoñ (WRYPT1 p. 302).
Mahé is a typical western French spelling, while Mahieu is more typical of Normandy and Picardy. The diminutive form Macelin- can also be a hypocoristic of any of various names beginning with Old Frankish madal, from Old High German, Old Saxon mahal 'council, meeting'.