my great grandfather charles was born illegitimately, to ann malcolm and charles findlay, in 1856. whilst he did not acknowledge the child, she put his name on birth certificate and called him charles after him.
That is not possible.
The Regulations under the provisions of the 35th section of the Registration Act state: "In the case of an illegitimate child, the Registrar must not enter the name of any person as the father, unless at the joint personal request of the mother and of the person acknowledging himself to be the father, who, under these circumstances, shall sign the Register, as informant, along with the child's mother, and shall be registered as the father, the word Illegitimate being added to the child's name."
In other words, the law does not allow the mother of an illegitimate child to put the name of the father on a birth certificate unless he acknowledges the child by accompanying her in person when she goes to register the birth, and signing the birth certificate alongside her.
It is, of course, perfectly possible for her to name her child after its father, even if the father does not acknowledge the child, and in fact that is quite common when the child is a boy.
If a court subsequently finds the paternity of an illegitimate child whose father has not acknowledged paternity at the time of registration, an entry is made in the Register of Corrected Entries, and cross-referenced from the original birth certificate. The original certificate is not altered.