If you had looked in
https://www.irishgenealogy.ie/en/ you would have found their marriage certificate. They were married in the Presbyterian Church, St Johnston, in the parish of ?Taughboyne in County Donegal on 27 October 1890. William Begley was a mechanic, residing at West Russell Street, Glasgow, son of Robert Begley, farmer. Both were of full age. Fanny was residing at Ballybigley, daughter of John McLean, shopkeeper. The witnesses were John McLean and Rebecca Bell, and the marriage was registered in the registration district of Strabane.
I see that in 1901 Fanney (sic) was 29, suggesting that she was born in 1871/1872. There is a birth of a Fanny McLean to John McLean and Sarah Kincaid in Greenock on 8 January 1871.
Noting that in 1901 William and Fanney had a daughter Sarrah F, full name in 1911 Sarah Florence, it looks possible that these might be Fanny's parents.
Robert Begley was born at Shellbrook, district of Ramelton, County Donegal, on 17 November 1890. Father's address given as Great Russell Street, Glasgow.
Sarah Florence Begley was born on 17 November 1895 at Shellbrook, district of Ramelton, County Donegal. The birth was registered by Maggie McLean, aunt, Shellbrook.
William Begley was bon on 2 March 1911 in Londonderry.
In 1901, at Shellfield, Rathmelton, Donegal, were
John Maclean, head, 58, grocer
Sarah Maclean, wife, 50
James Maclean, son, 27, born Glasgow
and Maggie, 25; John, 23; Evelyne, 13; Albert, 12; and Sarah, 10, Maclean
and Jane Kincaid, niece, 4
all except James born in Donegal.
Albert McClean, son of John McClean, Shellbrook, and Sarah Kincaid, was born on 1 July 1888 at Shellbrook, district of Ramelton, registration district Milford, County Donegal.
So your Fanny may have been born in Scotland, but she was actually Irish.