Some relevant comments here about names in birth indexes:-
www.rootschat.com/forum/index.php?topic=771498.0
If the male Wood child had died at birth or soon after he would be in the death index for Q1 1901 so it looks like he lived. An informal adoption was arranged for the Holroyd Wood child who was born in Liverpool in Q1 1901 so he could be the male Wood child. The only parent name on his 1904 baptism is Wood so presumably his mother's surname was Wood.