This is the birth reg for the butcher's son:
PALMER, THOMAS MOORE
GRO Reference: 1846 J Quarter in HOLBORN UNION Volume 02 Page 167
So, no middle name
but he is Thomas William at his baptism:
https://www.ancestry.co.uk/imageview...bc&pId=2032564
There's a marriage in 1844 for the parents, Thomas and Ann, though Thomas is a cheesemonger rather than a butcher. I think it's the right one as birth regs for some of the other sons (Harry and George) have mmn Moore.
Given this boy was eventually given the middle name William, I would imagine that is him in New Dunston Street in 1861. I will have one more look for the rest of his family in 1861......