I was interested to see McBurney and Dundee mentioned (I assume Dundee, East Scotland). I was born in Dundee in 1975. and to the best of my knowledge my direct family are the only McBurneys in Dundee.
I know very little about my family. My Grandfather, James was born in Belfast, Northern Ireland in (about) 1904, he moved to Leslie, Fife, Scotland in his early 20's and worked as a flax mill forman, where he met my grandmother, Agnes Michie, they had one son, my father, also James. My father moved once married to Dundee in 1973. I was born in Dundee in 1975, my sister Leanne in 1977 and my brother Scott in 1989. I have a daughter, Fay and my sister a son, Jake McGuire. I now live in Larbert, Stirlingshire although my Father, Mother, Sister and Brother all still live in Broughty Ferry, Dundee and my Grandmother in Leslie. As far as I am aware there are no other McBurneys in Dundee and very few in Scotland at all. I have never met anyone with my surname (not directly related to me).