Some clarification, Coinneach meant 'comely' originally - I suppose 'handsome' is more accessible or something, though I think that should be changed and if people need to run to their Websters to look up 'comely' then good - perusing a dictionary is becoming a lost art form ;o) In modern Scots Gaelic is cuanna/cuannar, in Irish cuanna which means 'fine' as well as 'handsome'. In modern language, còinneach which looks identical to coinneach actually means 'moss' which in Irish is rendered caonach.
Also coinneach is just Gaelic, not Irish. Scots and Irish Gaelic are closely related but often differ in formation of specific words. The surname form was actually Mac Coinnich, Scottish through and through. The Z in the modern MacKenzie form represents the medieval letter yogh, pronounced as a y glide at the time.