FTDNA has a number of Group Projects and Hagan(s)/Hagin/Hagen is one. It has approximately 112 members (September 2023). For haplogroups, there are 9 members at R-M222+, 7 at S588+ and 4 at BY11733+. 45 members are listed at R-M269+ (TMRCA about 13k years ago) with 39 others, such as R-FT137091 that diverge below P312, some 5k years bce and are now located west of Cookstown, County Tyrone. There is a O´Hagin (USA), a O´Hagan, Ireland with J-M172 haplogroup and one O´Hagan, Ireland, R-M269.
The Dal Cuinn Group lists 1 Hagan at haplogroup R-ZZ87+, 3 Hagan, 1 Hagen and 1 Fagan at R-FT165098+. There are no O´Hagan listed.

In the image below I have edited a small section of data from FTDNA´s Y-DNA Group Project: Cenel Eoghain - R-588 -> FT135097, Cenel Fergusa. The table compares member´s STR results. Where there is a non-results agreement among members I have put their value. The final mismatch values are given to the right as are the haplogroups. Underneath is the current haplogroup table. Some tentative dates are: FT165097 300ce; FT165098 650ce and FT135792 800ce.

I´ve wondered for a while, the relationship between the Druids and the Brehons wthin the pre-Christian Gaelic speaking Celtic Irish society. The early Irish Druids were perhaps the earliest priests in Europe. They were healers who used plant based remedies for their patients; they were law keepers and judges; they associated with Bards. Bards travelled around the country as musicians, poets and they told tales of such events as battles - they acted as historians. At that time Ireland was forested and trees were important to the Druids´ philosophy.

The Brehons were successors to the Druids and were well respected professionals as arbitrators and judges. They were educated to interpret Brehon law that was passed orally from one generation to the next. It is thought Brehon Laws may have originated during the Iron Age. It was not until the 7th century CE that Brehon laws were written for the first time. Many Brehons were freelance moving among and acting for different clans. Others were hereditary Brehons and were leading members of Irish society. These are some of the hereditary Brehon families: MacEgan - in Connaught, Leinster and Ormond; O´Doran - Brehons to MacMurrogh, Kings of Leinster; MacClancy of Clare - Brehons to O´Brian, Kings of Thomond & Fitzgerald, Earls ofDesmond plus other great families of Munster; O´Breslin of Donegal - Brehons to Maguire, lords of Fermanagh. Also were O´Hagan of Tullaghoge, Tyrone, Brehons to O´Neill, princes of Tyrone.

Further reading:
Druids & Brehons - Irish History
Druids - Brehon Law
Ireland´s Welcome to the Stranger by Asenath Nicholson is a good read about the Great Famine of mid 19th century. (To put in time context, that was ending in about as many years before I was born, to how old I am now)!
Brehon (Wikipedia)

Fosterage
The O´s were sufficiently high in society that they ostered Donnell

• Health and genetics

  Below is my method of finding my genetic data for any medical compaint I want to investigate. It is a method; others may use other ways.
  Whenever I read about a health issue I try to find its genetic component. I read of a sad case where a person took his own life after years of battling with bipolar depression. Entered "bipolar depression genetics genes SNPs" into google and National Institute for Health (ncbi.nlm.nih.gov/.... excellent website) gave SNP rs1006737 in the gene CACNA1C is the most studied variant associated with the disorder.
  First I go to SNPedia - it was recognised but without details of chromosome or location. Next try another ncbi site: National Library of Medicine. First ensured it was set to GRCh38 then entered thr RSId into the search box. Not found. Luckily the gene CACNA1C was given. Entered that and it was displayed with the RsId. Hovered over Rs10066737 and the location was displayed - chr12 2236129 location
  

  

   

  Finally I ran my IGV_2.16.2\igv-launcher.bat file then opened my Nebula Genomics WGS (whole genome sequence) BAM file. The result is shown in the screenshot below:

  

  Note: The details given above are my method - same applies to any genetic health complaint.

• Further details of my oldest known relative: John & Sarah Ann Hagan family was the only one living in Ballybay during the mid 19th century, so the 1877 death certificate of a John Hagan, a baker of Balllybay is gg grandfather John.

  
  John is recorded as being buried at Christ Church, Ballybay (church of Ireland), but there doesn't appear to be a headstone.
  Information kindly given by Monaghan County Library, Clones, Monaghan, Ireland.

• Hagan and O'Hagan are not common surnames. Below gives some data for the island of Ireland and globally.

  

   

• I've read that many ex-Gaelic clan families dropped their O´ whilst Oliver Cromwell was the Lord Protector, (1649-1653) so they sounded more "Enlglish" and could have a better life.

• In 1617 Hugh O´Neill gave Henry O´Hagan his Will should he die. Even at that time, after the destruction by Mountjoy in 1603 the Gaelic rather than English names were still sometimes used. The original Will, pre August 1617, Henry O´Hagan was written as Enri O Agán.

• Main software used: FTDNA from having Big-Y; Nebula Genomics 30xWGS (whole genome sequencing). Both of these have been purchased - I have no commercial links with either of them. To read the BAM file I use IGV_2.16.2, interactive genomics viewer, from igv.org. It is free to use and runs on both Windows and Mac (using Apple´s Rosetta Software).
  Other software is genetichomeland.com
  snpedia.com/index.php/rs1234
  ybrowse.org/gb2/gbrowse   Says not secure. It is ok, not updated to https.
  https://www.ncbi.nlm.nih.gov/genome/gdv/browser/genome/?id=GCF_000001405.40.