Here's an example of trying to think of all the possible variants of our name, though surely this is a 'deviant' version. In Ancestry.co.uk I searched for Mc Hagart (gap between Mc and H...) and only one result appeared, a family in the 1871 Scottish Census at 14 St. Andrew Street, Greenock East. As I hadn't got them in my Census Index I started to enter them - there were parents and five children. Just the two youngest had been born in Greenock, Scotland, all the rest in Ireland. (Would that they had put place names, and not just 'Ireland'!). My first thought was that, with the exception of the two youngest, I could start a 'virtual' 1861 Irish Census! Then it dawned on me that I was entering five of the nine children of none other than my own great-great-uncle born in Ballycloughan! This was a family that spelled their surname, to my knowledge, eight different ways, maybe because they lacked the schooling in a 'normal' or 'inherited' spelling. John was a Labourer, though by 1890 Mary his wife appeared to be operating as a self-employed Grocer!
They must have moved from County Antrim to Greenock about 1860, between the births of Elizabeth and Mary, by which time their eldest child Ann Jane must have 'left home', though it is probable that she too moved to Scotland for it is there that she had married the year before. The seven in the 1871 Census are:
John, 42, Labourer, born Ireland;
Mary, 38, wife, born Ireland;
Agnes, 17, Factory Girl, born Ireland;
Margaret, 14, Factory Girl, born Ireland;
Elizabeth, 11, Scholar, born Ireland;
Mary, 8, Scholar, born Greenock;
Janet, 5, Scholar, born Greenock.
A question remains: is the Agnes Mc_Haggart, who is in the 1901 Census for Scotland, and is the only example of this double 'g' spelling, the same Agnes as above in the 1871 Census? She was born 1855, aged 46, said to be born in Govan and living in 1901 at Barleyhill, Gl(stet). Govan Head, Falkirk, Stirlingshire. Living with her was Alexander, aged 26, born 'Greenah' (Greenock?), a Labourer. Ah, no! I have just realised that the Agnes in the 1871 Census died in 1900! So I'm afraid I do not know where this second Agnes and her son Alexander fit in!