Yes, we do! And I have no idea why Edwin played around with his names

Was he trying to hide his identity or what was the purpose I wonder.
Marion Shaw seems more straightforward.
Her birth:
Marion Shaw
Birth 8 Mar 1857 Govan, Lanark
Father: William Shaw
Mother: Marion Mcgregor
By 1871, the family are down in Birkenhead so she is well placed for that 1877 marriage:
William Shaw 42 Boiler maker b. Glasgow
Marion Shaw 38 b. Scotland
Marion Shaw 14 b. Scotland
William Shaw 8 b. Ireland
Barbara Shaw 6 b. Ireland
Ellen Shaw 4 b. England
Robert Shaw 9 months b. England
I haven't looked for the family's 1881 entry but in 1891, William, boiler maker, wife Marion and some of their children are back in Govan and living at 78 Queen St.
So, as far as we can see, her family is easy enough to find with the details we have.
The middle name of McLean for Marion Shaw comes from her maternal grandmother, Marion McLean.
Monica