The name McMahon

Irish: an Anglicized form of Gaelic Mac Mathghamhna, a patronymic from the byname Mathghamhain — literally “good calf”, a kenning for “bear”. This was the name of two (unrelated) chieftain families, in counties Clare (Thomond) and Monaghan (the kingdom of Oriel). See also Mahon and Mahoney. In northern Ireland it is sometimes Anglicized as Matthews, since Matha was the Irish form of the Biblical name (see McMath). In Scotland, Matheson was used to translate both of these surnames.

Mahon

Irish: a shortened Anglicized form of Gaelic Mac Mathghamhna, “son of Mathghamhain” (see McMahon). Compare Mahoney, which has a similar etymology. There has been some confusion with Mohan and Mahan. Irish: from Ó Mácháin, a variant of Ó Mocháin (see Mohan). French: a habitational name from Mahon in Gironde. French: from the Old French female personal name Mahon, a derivative of Mahaut, vernacular form of Mathilde, from the ancient Germanic personal name Mahthild — composed of the elements maht “might” and hild “battle”.

— Family name meanings via Ancestry