McKenzie is Scottish. It is the Anglicized form of Gaelic Mac Coinnich. it's patronymic (based on the name of one's father, grandfather, etc) from the personal name Coinneach meaning 'comely'. Source: Genealogy.familyeducation.com
Irish
My father and three generations before him were born in ireland but I was always brought up to be a true Scot, we are proud Mckenzies or MacCoinnichs and I'm family on both sides having McUaid, McFarland, McWhir, Quinn, Sharkey. This tells me we are both as seperate countries as one and united in blood as anyone. God bless Ireland and Scotland, For as belonging to both I am the proudest woman on Earth and no other country on Earth could fulfill to me what I get out of living here in Scotland and having Ireland in a days distance, I just must be the luckiest woman alive. Slainte XX