The Irish surname Reagan (or Regan) is an anglicized form of the Gaelic surname O'Riagain.  It is a widespread name which came from several ancestors.  One clan came from the Dublin area and were part
of the "Four Tribes of Tara."  Another clan was located near Fermoy in County Cork and the third were located in county Tipperary..  The O'Riagain clan is important in Irish history because they were very active against the Viking invaders.  They can trace their origins back almost a thousand years to a nephew of Brian Boru, one of the great kings of Ireland. 
The Reagans emigrated to America before the time of the Great Famine in Ireland.  The Reagan name is seen in the military rosters of the American Civil War, a Anthony O'Regan was a Bishop of Chicago, another Regan was a progressive jurist in Texas. 
The most well known is Ronald Reagan, the 40th President of the United States, whose family came to America from county Tipperary.
In the Tipperary area the family name is pronounced "Ray-gan."

However, in Ireland today "Reegan" is the most common  pronunciation.
2004 Reagan Family Reunion

REAGAN:
THE FAMILY NAME