George was born on 4th August 1892 and there are two registered in that year in Birkenhead. One was George Oldfield Walker, mother's maiden name Corlett but he moved to Liverpool and died in 1937.
The other George, mother Keeley, is presumed to be the one on the 1939 Register with wife Jane. Unfortunately, I can't see a baptism.
Sarah Jane Keeley married Edward Brannigan, in Liverpool in 1891.
In 1901, George Walker is shown as the son of Sarah Jane Brannigan, married but no husband, but his siblings are Brannigan.
In 1911, Sarah Jane is married to Edward Walker and all of the children are Walker, including those previously Brannigan. Sarah and Edward had been married 18 years and so it looks at though Edward Brannigan and Edward Walker might be the same person.
Although all of the children in 1911 are Walker, they seem to have been registered as Brannigan - strange.
I imagine that the marriage may show his father as Edward but it would be interesting to see the birth certificate.
David