Connor is the first name used by Assassin's Creed III's protagonist, who was born Ratonhnhaké:ton.
The character is a Kanien'kehá:ka, or Mohawk, Assassin whose story unfolds during the American Revolution. He adopts the name Connor after leaving his village and seeking training from Achilles Davenport. The game follows his conflict with the Templars and his efforts to protect his people amid the upheaval of the eighteenth century.
Connor's birth name is Ratonhnhaké:ton, while Connor is the name most commonly used in the game's English-language presentation. He is also the son of Haytham Kenway, the Templar protagonist of the opening sequence, creating a family connection that drives much of the plot.
Edward Kenway belongs to Assassin's Creed IV: Black Flag, and Shay Cormac is the protagonist of Assassin's Creed Rogue. Haytham is Connor's father, not the answer to the question asking for the son's commonly used first name.