I think at the time of adulthood, the child can choose which name they want to carry on.
My main question is why does your name get to be used for the child? She carries the child, bring it into life, births it, feeds it from her body, gives up her body for at least a year to provide for this child from conception to at least 3 months of breastfeeding, which many go a lot longer, and all you did was have a sperm lucky enough to hit the egg. So why does the child get your last name and what is the father’s line the important one to carry down while the mother‘s line can be ended?