I suspect that the original name was HEGEMANN. One of you ancestors may have added the second G to preserve the pronunciation (obivously withh little success). But I have nothing to back this up. If this is true, there are at least two interpretations of the name:
HEGEMANN 1. Habitional name for someone living in or near a place called Heeg or Hege (there a various places by that name in Germany) 1. A Westphalian topographic name for someone who lived in an enclosed (i.e. fenced) area, Middle High German hagen + man ‘man’. Or for someone who lived by a hedge or by the boundary of an enclosure.
There is also the name HEGEMAN, and here I find the double G again: Dutch: habitational name for someone from a place called Hegge(n) or ter Hegge(n), derived from a word meaning ‘hedge’.
This is taken from: Rosa und Volker Kohlheim, Familiennamen, Mannheim 2000 P.H.Reany, A Dictionary of English Surnames, Oxford 1997