Origin and Meaning of the Surname:
Listed below are the entries from two authoritative works on the derivation of the surnames. I have expanded on the texts to give their sources in full, hopefully putting their brief notes into English without inadvertently changing the authors intent in so doing.
The Dictionary of English and Welsh Surnames by Bardsley allocates the name to the group of surnames showing relationships in that it is derived from a baptismal names meaning the "son of Ismay". What is really unusual is that Ismay is a somewhat rare girl's name found in the thirteenth century. He concludes by noting the name managed to survive and become a surname, and still lives.
The earliest examples he quotes include "Ysemay Vidua and Isemay Egleberd both found in the Hundred Rolls for the County of Oxford in 1273; Richard fil Ysmay found in the Hundred Rolls for the County of Lincolnshire and finally Ismaya Hibernicia in what Bardsley quaintly terms Documents Illustrative of English History.
P.H. Reaney's Dictionary of British Surnames (second edition amended by R.M. Wilson) notes the earliest occurrences of the name as Ysemay de Mult in 1275 in the Royali Hundredorum for Lincolnshire; Ralph Isemay, Hyssmaye found in the Descriptive Catalogue of 13th century Charters for Sheffield, Yorkshire and William Ysmay in the 1327 Subsidy Roll for Derbyshire.
Reaney continues by postulating that this somewhat rare woman's name might derive from a possible unrecorded old English word Ismaeg, though he notes that "Is" is unknown in old English names and "maeg" is found as a second theme in only three late names as illustrated by Idemay la Frye in th e1327 Subsidy Rolls for Somerset. Reaney then states that the equation of the earliest example of Isemay (1227 Assize Rolls for Buckinghamshire) with Isemeine (from which the surname Enemey is derived) suggests a continental origin. He notes that "Is" occurs in a number of old German names and quotes Forstemann's derivation of "Macharias" rom the root "Mag", which is related to the Old High German word "magan" meaning might. He also notes that Forssner suggest the Old French word "Maissent" may contain the same first element, from the Old German Magisand, Megisind, and hence he concludes that Ismay may perhaps be form Old German "Ismagi or Ismegi" meaning "iron might or strength"
George Edward Cokayne’s in the complete peerage of England, Scotland, Ireland, Great Britain and the United Kingdom, extant, extinct, or dormant, Vol. 3 provides
Of uncommon and remarkable women's names (c) that of Idonie or Idoine, Remarkable latinized as Idonea, was borne among others both by a daughter of Robert, women's names. Lord Clifford, and of William, Lord Leyburne, both Cumberland people. In the will of Henry Lord Percy, husband of the former, dated 1349, his wife is called Imania (Ismania), and though there are not many instances of this name, it is stated to be the origin of the surname Ismay, now well known in shipping circles, just as Iseult or Isolt (Welsh Esyll, lat. Isolda) is preserved in the surnames Issot, Isitt, and in the place near Dublin, Chapel Izod. The natural Impression of anyone approaching the subject without previous study would be that names like Idoineand Joyce were corruptions of theLatin Idonea and Jocosa, whereas it is more likely that the former are the originals and the latter copies or fanciful translations.