Irish (Ulster): Anglicized form of Gaelic Ó hÍr, meaning ‘long-lasting’. In Ireland this name is found in County Armagh; it has also long been established in Scotland.
Irish: Anglicized form of Ó hAichir ‘descendant of Aichear’, a personal name derived from the epithet aichear ‘fierce’, ‘sharp’. In Ireland this name is more commonly Anglicized as O’Hehir.
English: nickname for a swift runner (possibly a speedy messenger) or a timorous person, from Middle English hare ‘hare’. However, the surname Ayer and its variants was sometimes recorded as Hare.
It's also a topographic name from an Old English hær ‘rock’, ‘heap of stones’, ‘tumulus’.
French: according to Morlet, an occupational name for a huntsman, from a medieval French call used to urge on the hounds, or, in the form Haré, from the past participle of harer ‘to excite, stir up (hounds in pursuit of a quarry)’.
Source: Dictionary of American Family Names ©2013, Oxford University Press