Short answer. No. The same provision that lets a recognised child use the father's surname keeps parental authority with the mother, and says so in the very sentence before. The surname and the authority are separate questions, so allowing the one concedes nothing about the other.
What the law says
Illegitimate children shall use the surname and shall be under the parental authority of their mother, and shall be entitled to support in conformity with this Code.
RA 9255, Section 1 — Surname Of Illegitimate Children. Read the full provision →
What the law says
illegitimate children may use the surname of their father if their filiation has been expressly recognized by the father
RA 9255, Section 1 — Surname Of Illegitimate Children. Read the full provision →
The two are separated in the text itself
Illegitimate children shall use the surname and shall be under the parental authority of their mother, and shall be entitled to support in conformity with this Code. The exception that follows reaches only the first of those three things: illegitimate children may use the surname of their father if their filiation has been expressly recognized by the father. Nothing in it touches parental authority. The law lifted the surname out of the package and left the rest of the package where it was, which is precisely the answer to this question.
The surname reflects recognition; it does not confer anything
It helps to see the sequence. The father recognises the child, and the surname becomes available as a consequence of that recognition. The name is therefore a marker of a relationship already established, not an award of anything to the father. Whatever he gains, he gained by recognising — and what recognition brings him is chiefly obligation, since it is the basis on which support is claimed from him and on which the child shares in his estate.
A father can still go to court, with or without the surname
This is the honest qualification. Custody, visitation and access are decided on the child's best interests, and a recognised father can bring that case whether the child carries his surname or not. So refusing the surname is not a defence against a custody application, and granting it is not a concession in one. If a mother's real concern is a future dispute over the child, the surname is close to irrelevant to it — the decisions that matter are about parental authority, and those are answered by the first sentence of this provision.
Decide the surname on its own merits
Freed of the custody worry, the question becomes a practical one about the child. Consistency across records is what matters most: a name used at school, on identification, on a passport and on benefit claims should be the same name, and changes made late leave a trail in two names that has to be reconciled at every counter for years. The civil registrar's implementing rules prescribe the documentation for entering or changing the surname, so ask that office what it requires before deciding — and weigh the child's own preference where he is old enough to have one.