One of those lovely words that is sooooo obscure in origin. This link has some good information:
The Scot Abroad: Chapter 5 - Influence of Manners - Part 4
Hagmané, Hagmonay, n. [Obscurely related to OF. aguillanneuf, haguimenlo, etc., mod. Norman dial. hoguinané.] Hogmanay , the New-Year’s Eve gift; the word shouted in soliciting this. — [January 3rd], William Pattoun delatit to haue been singand hagmonayis on Satirday; 1604 Elgin Rec. II. 119. It is ordinary among some plebeians in the South of Scotland to go about from door to door upon New-years Eve, crying Hagmane; 1692 Presb. Eloq. (ed. 2) 82.
Retired English Teacher