What I have is as follows:
My Grandmother Ann Maria Dougherty was born about 1864 in Buncrana (I don't have a birth certificate but calculated from age at marriage, death and censuses). Her parents were James Dougherty and Ann O'Donnell. On her English marriage certificate her father is Dougherty, but on two of her brothers marriage certificates in Scotland, the parents are both named as Docherty.
Ann Maria Dougherty came to England, and married my grandfather James Lynch in Bootle. One brother James also came to Bootle and was a coal merchant. But he marrried a girl from Duntocher, Kirkpatrick.
Another brother Patrick went to Scotland and married a Catherine Lynch from Ireland !
The youngest bropther Joseph also went to Duntocher.
I find the Scottish marriage certificates very informative because they give the bride/groom's mother and father details with maiden name of mother.
