Have you seen that there are two births registered in West Derby of Goodman children with MMN Ward? The first, in 1919 is also indexed under Ward, implying that the parents aren't married. The second, in 1922 is indexed only under Goodman.
The following is not conclusive, but might be of interest.
There is a 1921 marriage in West Derby of an Edwin Goodman and Theresa Neish.
I can't see a Theresa Neish anywhere in 1911.
There don't appear to be any Goodman births registered with MMN Neish
In Dec Q 1911 a Theresa Wood married Joseph Neish in West Derby. Three births follow this marriage, the last in 1918 (this child died soon after birth).
I can't see a likely death of Joseph Neish.
The only Theresa Wood in West Derby in 1911 is aged 23 (so born 1887/8)
A Theresa Goodman dob 8 Feb 1888 died in 1974 in Alyn & Deeside district.
To sum up, I think Theresa Wood married Joseph Neish and then Edwin Goodman. She might have felt she had reason to alter her maiden name to Ward.
[I'm becoming more doubtful now I've typed it all out, but you never know]