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If the spelling is your problem, here's a breakdown.
Docherty, the commonest spelling in Britain, found overwhelmingly in Scotland. Rare in Ireland.
Doherty, the commonest spelling in Ireland, also found in Scotland and England.
Dockerty, best represented in the North of England. Not even noticeable in Ireland or Scotland.
Dogherty, rarer spelling found in Ireland.
In Irish it's O Dochartaigh for a gent and Ní Dochartaigh for a lady. The homeland is Donegal, whose emigrants usually headed for Scotland, particularly Glasgow and Dundee. Docherty, however, seems to be strongest in the Argyll and the Western Isles. There were Odochertys in Islay in the early 17th century.