Fallon
An Irish surname most often treated as an Anglicized form of a Gaelic family name, though some writers also suggested other origins.
The #2,994 most common surname in the United States (2010 Census) — about 1 in every 25,785 Americans shares it.
Etymology
In Irish genealogy, Fallon is commonly explained as an Anglicized form of Gaelic Ó Fallamháin / Ó Fallón-like spellings, ultimately tied to a personal name. The historical excerpts you supplied also point to a Gaelic family-name source, with Woulfe listing Fallon alongside related Irish forms such as Falloon and Faloon. Some older writers proposed other explanations, but the Irish derivation is the strongest broad explanation for the surname as used in Ireland and among Irish emigrants.
History
Fallon is well established in Ireland and became more visible elsewhere through Irish migration, especially to Britain, the United States, Canada, and Australia. Nineteenth-century surname writers discussed it at length, sometimes with conflicting guesses, but later Irish onomastic work generally places it among anglicized Irish surnames. In modern usage it is especially associated with Irish-American families.
Origin
Regions
Variant spellings
Fun fact
Older surname books sometimes argued about whether Fallon was Irish, Gaelic, or even a corruption of another form—showing how tricky Irish surnames could be for early lexicographers.
From the historical record
“Descendant of Fallomhan [v. O'-, and Fallon] OFFER 1 OFFOR I 3ssim. forms of Orfeur.q.v. OFFLEY (Eng.) Bel. to OfQey (Herts, the”
— Surnames of the United Kingdom: a concise etymological dictionary (2 vols in 1)