Gilbertson/Thompson marriage 1860?

I have posted this enquiry here as I am not sure where the marriage, if any, took place.
1861 census.
William Gilbertson 28 Police Costable private. B Scotland
Mary Ann Gilbertson 25 b Whitehaven, Cumberland
Thomas Gilbertson 1 b South Shields, Durham.
Living West Street, Westoe, Durham.
Ref RG09/3786/36 page 5
GRO Index.
Gilbertson, Thomas. 1859 Dec South Shields. Mmn Thompson.
(Subsequent children also had mmn Thompson)
I have not been able to trace a matching marriage.

Family search.
Baptism. Mary Ann Thompson 27 August 1837 Whitehaven. Parents Robert and Alice
Marriage. 18 May 1834. Robert Thompson/Alice Braithwaite or Thompson. St Bees, Cumberland.
In1841 Alice and Mary were living in household of Robert and Sarah Grahm, St Bees. No sign of Robert.
In 1851 Mary was living with her grandmother in Whitehaven, I have not been able to identify Alice with any degree of confidence.

Is it possible to join up these dots?

In the 1881 Census it says that William Gilbertson was born in Annadale, Gretna Green. Class: RG11; Piece: 5118; Folio: 158; Page: 35.

It's possible that William and Mary Ann married in Scotland. You would need to look on Scotland's People site to find out if there was a marriage there.

Its possible that this is William in the 1841 Census: Gretna - Parish: Gretna; ED: 7; Page: 3; Line: 1474; Year: 1841.

Mary Ann died in 1920, and in the 1911 Census she is a widow living with her son Robert and granddaughter Alice. Unfortunately she wasn't one of those widows who helpfully filled in the marriage columns even those as widows they were not supposed to.

I have searched Scotland's People for evidence of a marriage without success
I found the 1841 census entry. There is also a possible reference in 1851. William Gilbertson, 20. Born Scotland. Farm servant. Living Lazonby, Cumberland. HO107 2426/305
I was aware of granddaughter Alice. I think she may have been the daughter of the unmarried Jane. Was the choice of name a coincidence or is it of relevance?

Lazonby is Penrith so its all within the right area.

I wonder if they were not married..... In 1858 a William Gilbertson married in Hexham either Jane Henderson, or Agnes Lishman.

I agree that the most likely explanation is that William Gilbertson and Mary Ann Thopson did not marry, but there are two remote possibilities.
a) Mary Ann had been married previously.
b) Her mother, Alice, remarried and Mary Ann adopted her step-father's name.
Having said that, I can find nothing to substantiate the theories.

I have now deduced the in 1851 Mary Ann was living with her grandmother, father and brother. Her father was described as "widowed"