Hi
From the 1851 census I see Daniel Taylor, father, aged 69 born Kempton Hampshire, Sophia Taylor, mother, aged 56 born Hatfield Hertfordshire, Daniel Taylor, son, aged 24 born Chelsea & William Goodman Taylor, son, aged 21 born Chelsea.
The marriage for Daniel & Sophia is on Family Search.
https://familysearch.org/pal:/MM9.1.1/NKNZ-4PJI'm assuming William was given his mothers surname for his second name as there's no reason to suspect he was born out side of Daniel & Sophia's marriage.
Unfortunately I can't see any records for Hatfield or near by on FS to find Sophia's parentage so it might be worth you contacting Herts Archives & Local Studies, (HALS)
As our Goodman's are in the Rickmansworth & Watford area of Herts I don't think there is likely to be a connection but you never can tell.
Maddie