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Hi Everyone, I've been banging my head against a wall and it hurts! Please, can anyone help?

Rebecca HAMILTON was born 28 Feb 1874 Newtownstewart CCounty Tyrone Northern Ireland daughter of James HAMILTON and Isabella HAMILTON. I can find her on the 1901 census and 1911 possibly as a servant. We known she was buried with her mother and father but with the name Becky BROWNE (Not on gravestone). I've been trying to find a marriage to a **** BROWNE and there is one in the Strabane district in 1915. Ah I thought I'll look on the 1939 register then realised the Irish wouldn't have a need for that so maybe a 1939 register for Northern Ireland but cannot find one. So that is where I am in trying to find who the Becky BROWNE is in that grave. Any thoughts please?

https://civilrecords.irishgenealogy.ie/

Marriage of BENJAMIN BROWNE and REBECCA HAMILTON
on 14 July 1915

Party 1 Name BENJAMIN BROWNE
Party 2 Name REBECCA HAMILTON
Date of Event 14 July 1915
Group Registration ID 1693649
SR District/Reg Area Strabane
Image(s) 1 2

From image -
Married at Baronscourt Parish Church
Benjamin - age 43 a Carpenter, s/o William also a Carpenter
Rebecca - age 39 d/o =Janes, deceased.
Both of Baronscourt at time of marriage
Witnesses - Thomas and Mary Hamilton

If it's her then she's knocked a couple of years off her age!

Becky is surely just a variation/nickname of Rebecca

She has a brother Thomas and Sister Mary by the looks of it who are probably the witnesses -

1901 census
Residents of a house 4 in Ballyrenan (Baronscourt, Tyrone)

Surname Forename Age Sex Relation to head Religion Birthplace Occupation Literacy Irish Language Marital Status Specified Illnesses
Hamilton James 55 Male Head of Family Church of Ireland Co Tyrone Watch Man Read only English Married -
Hamilton Isabella 56 Female Wife Church of Ireland Co Tyrone Seamstress Read only English Married -
Hamilton Rebecca 26 Female Daughter Church of Ireland Co Tyrone General Servant Domestic Read and write English Not Married -
Hamilton James 21 Male Son Church of Ireland Co Tyrone Agricultural Labourer Read and write English Not Married -
Hamilton Robert 19 Male Son Church of Ireland Co Tyrone Agricultural Labourer Read and write English Not Married -
Hamilton Thomas 19 Male Son Church of Ireland Co Tyrone Agricultural Labourer Redd and write English Not Married -
Hamilton Andrew 17 Male Son Church of Ireland Co Tyrone Post Man Read and write English Not Married -
Hamilton Joseph 14 Male Son Church of Ireland Co Tyrone Agricultural Labourer Read and write English Not Married -
Hamilton Mary 11 Female Daughter Church of Ireland Co Tyrone A Schoralar Read and write English Not Married -

https://www.irish-genealogy-toolkit.com/1939-national-register.html

Explains about access to the NI register (found by googling)