You have to look at records with an open mind, things are not always what they seem.
It was very common for children to take their stepfather's name, not just illegitimate children but those of widows who remarried. You often find a stepfather, or even a grandfather or uncle named as father on the marriage of an illegitimate person, it was simply to conceal the illegitimacy.
Youngest child + 2 elder grandchildren of my 3x GGM were on 1871 census with their step-grandfather's surname and listed as his children. GGGGM's youngest child was illegitimate, born after 1st husband disappeared from her life and from records, and 4 years before she married 2nd husband. The grandkids were also illegitimate, elder born when their mother was 17. The grandchildren's mother had married 1870 but her husband wasn't father of her children. The step-grandfather died before 1881 census. GGGGM's youngest daughter and grandchildren were still with her on 1881 census under their own surnames and with correct relationships.
Neither 3xGGM nor her husband seem to have been literate. Therefore I assume that they gave personal information on the census form verbally, either to their step/children or to someone else. They had recently moved to a different town, the home of GGGGM's new husband & his parents. Her mother & stepfather wouldn't have wanted a neighbour or a stranger to know their family history. My 3xGGM was young enough to have been mother of both her elder grandchildren.
The youngest daughter named her mother's first husband as her father on her marriage certificate as she had his surname. The father on marriage certs of the 2 grandchildren was a combination of their step-grandfather's first name + their surname. Each called a son after their made-up father. It's possible that their spouses didn't know the father's name was a fiction.
Always keep in mind that C.19th. English census records you are looking at are census enumerators' books, not household census returns, so information on them is at best second-hand.
One set of my grandparents were already married, both for the second time, with children from their first and second marriages, before 1911 census. Daughter of grandma's 1st marriage was on 1911 census return with granddad's surname. Her relationship was stated as his daughter. Columns for length of marriage and number of children born to present marriage were "adjusted" to fit with information given for children's ages and relationships. Grandad's age was incorrect on the census. (That was 4 fibs on the form.) His age was wrong on every census as he always aged by a few years less than 10 each decade so that by 1911 his age matched his younger sister in Ireland whose age had leapt by more than a decade.