https://en.wikipedia.org/wiki/Hennessey
https://en.wikipedia.org/wiki/Hennessy_(surname)
The Hennessy family name is an Anglicisation of Ó hAongusa (its form in the Irish language) which means descendant of Aonghus or Angus (a native Irish personal name meaning the chosen one).
The name is apparently an ancient one. The first hint of this is the Ó prefix which, along with Ua, means “grandson of”. Also, there is a character in medieval Irish mythology called Aonghusa who was supposed to be a chief of the Fir Bolg people. These were said to have lived in Ireland prior to the arrival of the Celts. Dún Aengus, a 2500 year old fort on Inishmore, one of the Aran Islands situated off the Galway coast, is associated with him.
There were numerous branches of the Hennessy clan in Ireland prior to the coming of the Normans and the leading one was based in Offaly. With the arrival of the Normans, the surname became scattered across counties Limerick, Cork and Tipperary. These also are the counties where the majority of the name is still found.
Today, the Hennessy name is best known for its association with a world famous brandy, the formula for which was discovered in the eighteenth century by Captain Richard Hennessy. He originated from Ballymacmoy near Mallow in County Cork and made his profitable discovery after his retirement from the French army (he had served in the Regiment of Dillon, and was medically retired after being badly wounded during the Battle of Fontenoy, 11 May 1745).
It seems there is not an active clan organisation for your name, at this time.
However, the revival of interest in Irish culture and heritage over the past 100 years has led to the revival of many Irish Clans. In more recent times, increased access to historical archives online, DNA testing and ease of travel to Ireland has led many individuals to explore their own genealogy and connections to Irish Clans. Some of these have gone on to establish Clan Associations in Ireland, the USA, the UK, Canada, Australia, New Zealand and anywhere that the Irish Diaspora has found itself.
Clans of Ireland Ltd invite those interested in Irish Clans to contact them with a view to explore the possibility of reviving your Irish Clan.