Fionn mac Cumhaill is said to be the posthumous son of Cumhall Mac Trénmoir of Leinster by Muireann, daughter of the druid Tadg mac Nuadat. His father is said to have died in the Battle of Cnucha which is said to have occurred in 225 AD. Thus, Fionn mac Cumhaill was born about 225 AD.
Fionn mac Cumhaill was first called "Demne Maol" by his mother, Muireann. 
Demne Fionn Mac Cumhaill (Finn Mac Cool) was a mid 3rd century Irish warrior, a poet and a seer around who have grown many legends that have enriched Irish mythology. Finn Mac Cumhaill and his father Cumhall Mac Trénmoir of Leinster led the Fianna who kept a watch on inlets and anchorages against the threat of invasion by marauding foreigners. 
Fionn is said to have died in the Battle of Gabhair which is said to have occurred about 284 AD.
Fionn mac Cumhaill, also known as Finn McCool, is a central hunter-warrior character in the Fenian Cycle, one of the four major cycles of Irish mythology along with the Mythological Cycle, the Ulster Cycle, and the Historical Cycle.
↑ 1.01.1 Silvester O'Halloran, A Rorg-Caṫa, or Martial Ode, Sung at the Battle of Cnucha by Fergus, Son of Finn, and Addressed to Goll, the Son of Morna; with a Literal Translation and Notes, The Transactions of the Royal Irish Academy , 1788, Vol. 2 (1788), pp. 7-17 (https://www.jstor.org/stable/pdf/30079248.pdf : accessed 24 Dec 2020)
↑Know that it was Cumhall son of Treanmhor, the fourth in descent from Nuadha Neacht, king of Leinster, who was his father, and that his mother was Muirn Mhunchaomh daughter of Tadhg son of Nuadha, druid of Cathaoir MorThe History of Ireland page: 331 by Geoffrey Keating Corpus of Electronic Texts Edition