This has prompted me to ask a question about English birth certificates in general.
In Scotland, an illegitimate child can only be registered under its father's name if the father accompanies the mother to the Registrar's when she goes to register the birth. In that case the certificate has both the father's name and the mother's name on it, and the birth is indexed under both surnames.
Does the same apply to English ones? Specifically, are they indexed under both names if both parents sign the original certificate together?
(I know a birth can be re-registered many years later if the parents eventually marry; this question relates only to the original certificate.)
I am not completely sure, your google search is as good as mine. I think at least it used to be that the father had to sign something or be physically present for his name to go on the birth certificate when parents were not married. I am not sure if that is still the case, I think I have heard single mothers say that they name the father on the birth certificate, but that might be with him present even now.
As far as I know, the birth certificate is only indexed under the child's given surname, so if the parents were not married and the father signed so that the child took his name, then the child's birth certificate would only be indexed under his name, just as any other birth.
I think you are saying that Rebecca knew what she was doing when she gave her name as "Thomasina Wilson", and no father named, on her children's birth certificates, as a hint to the children of who their father was if he refused to be named. That is what one person speculated. I think she gave a totally made up name so as not to shame her own family, and Samuel's family, and he had gone to sea promising to come back to marry her, which he did eventually, just after he qualified with his final certificate as a master seaman. This wasn't one accidental pregnancy, Rebecca had two children about a year apart, and these were the only children she ever had, and she was a young woman who married twice. Rebecca gives her occupation as "none" on the 1881 census when she was living with her sister and brother in law, so somebody was supporting her financially and presumably paying for her children to be well cared for elsewhere - as the other thread shows, Beatrice, age 4 on the 1881 census, was staying with a William Luckie, omnibus driver, and his wife. This was the heyday of the baby farmer, so Beatrice and Herbert must have been able to avoid that because somebody could afford to pay for decent care.
On Beatrice's birth certificate it says she was born in Chelsea. I would have to dig further to find out exactly where, and hence the circumstances.
I don't know how much you read of the other thread, but I don't think it was the same Samuel Park shown on the 1911 census as a 60 year old naval pensioner, because I looked at that original document and on it he gives his birthplace as Hampstead, which is a long way from Greenwich. That document also says he is a boarder, living with a Sarah White, head, widow, whose occupation is "washing, at home". I think the odds are that when Rebecca lists herself as a widow on the 1891 census, that Samuel was lost at sea. I haven't found death records for Samuel anywhere. And why would Samuel be living in a London boarding house in 1911 when the rest of his family, parents, brother and sister, had all moved down to Devon by then? I did read that deaths at sea are recorded differently, and finding them is complex.