Irish sounding names such as Henebry, Gogan and O'Dell are quite common in Ireland, yet none of them are of Gaelic origin. MacLysaght, Edward, Irish Families. We have a record for Maurice Henebry of County Limerick, the Diocese of Cashel. His will was made in 1739 and probated in 1760. Province of Munster.
Surname indicates Norman origin.
As with most genealogy searches, disagreements regarding the origin of the surname is common. Some accounts indicate the family came from Germany to Ireland. There is a village in the Palatinate called Henneberg. Henry Hennebery and his wife Mariah, both from Germany, were living in Franklin County, MO from the 1850 census. See the Norman invasion of 1169 for De'Alton or D'Alton and others.