Hay(s), Haye(s), Hayse and Hey Surname

Hays
Irish and English: variant spelling of Hayes 1–4.
Dictionary of American Family Names, Oxford University Press, ISBN 0-19-508137-4

Hayes
Irish: reduced Anglicized form of Gaelic Ó hAodha ‘descendant of Aodh’, a personal name meaning ‘fire’ (compare McCoy). In some cases, especially in County Wexford, the surname is of English origin (see below), having been taken to Ireland by the Normans.
English: habitational name from any of various places, for example in Devon and Worcestershire, so called from the plural of Middle English hay ‘enclosure’ (see Hay 1), or a topographic name from the same word.
English: habitational name from any of various places, for example in Dorset, Greater London (formerly in Kent and Middlesex), and Worcestershire, so called from Old English h?se ‘brushwood’, or a topographic name from the same word.
English: patronymic from Hay 3.
French: variant (plural) of Haye 3.
Jewish (Ashkenazic): metronymic from Yiddish name Khaye ‘life’ + the Yiddish possessive suffix -s.
Dictionary of American Family Names, Oxford University Press, ISBN 0-19-508137-4

Hay
Scottish and English: topographic name for someone who lived by an enclosure, Middle English hay(e), heye (Old English (ge)hæg, which after the Norman Conquest became confused with the related Old French term haye ‘hedge’, of Germanic origin). Alternatively, it may be a habitational name from any of various places named with this word, including Les Hays and La Haye in Normandy. The Old French and Middle English word was used in particular to denote an enclosed forest. Compare Haywood. This name was taken to Ireland (County Wexford) by the Normans.
Scottish and English: nickname for a tall man, from Middle English hay, hey ‘tall’, ‘high’ (Old English heah).
Scottish and English: from the medieval personal name Hay, which represented in part the Old English byname Heah ‘tall’, in part a short form of the various compound names with the first element heah ‘high’.
French: topographic name from a masculine form of Old French haye ‘hedge’, or a habitational name from Les Hays, Jura, or Le Hay, Seine-Maritime.
Spanish: topographic name from haya ‘beech tree’ (ultimately derived from Latin fagus).
German: occupational name from Middle High German heie ‘guardian’, ‘custodian’ (see Hayer).
Dutch and Frisian: variant of Haye 1.

Haye
Dutch and Frisian: from a personal name, Frisian Hajo, Germanic Haio; or from a short form of the feminine name Hadewig, composed of the elements hadu ‘battle’, ‘strife’ + wig ‘war’.
German: variant of Hey 4, 5.
French: topographic name from Old French haye ‘hedge’.
Scottish and English: variant spelling of Hay 1–3.
Dictionary of American Family Names, Oxford University Press, ISBN 0-19-508137-4

Hey
English (Yorkshire): habitational name from a place called Hey.
Dutch: topographic name for someone who lived on a heath, Dutch hei, heide.
German: metonymic occupational name for a grower or mower of grass, from Middle High German höu ‘grass’, ‘hay’.
North German (Frisian) and Dutch: from a Germanic personal name formed with hag ‘fence’, ‘enclosure’ as the first element.
South German: occupational name from Middle High German heie ‘ranger’, ‘warden’, ‘guard’ or a topographic name from Middle High German haie ‘protected wood’.
Dictionary of American Family Names, Oxford University Press, ISBN 0-19-508137-4