The ties between parent and child
Although the court has held that it’s important to maintain the link — through a shared surname — between a parent (typically the father) and a child, this should be considered in light of the ties and the amount (and quality) of contact between them, and the degree of commitment of the parent to the child.
This was held — as quoted above — by Lady Justice Butler-Sloss in Re W, Re A, Re B (Change of Name)  EWCA Civ 2030, who said that —
Where the child’s parents were not married to each other, … the degree of commitment of the father to the child, the quality of contact, if it occurs, between father and child, the existence or absence of parental responsibility are all relevant factors to take into account.
However, courts have held that even when the parents were married, the ties between father and child are still important. In Meek v Meek (1980) CA (where the parents had divorced), the Court of Appeal held that it was important to maintain the link with the father even when he had been convicted of manslaughter (having been charged with murder) and sentenced to three years’ imprisonment — given that the court was satisfied that the children would “continue to have access to their father”. Lord Justice Orr, in dismissing the appeal in that case, agreed with the judgment of the County Court below, in that —
… if [the children] were to use another name, it would be a strange thing for them when having access to the father and probably disturbing to them.
In Salter v Ashworth (1980) CA (where the parents had also divorced), the Court of Appeal upheld the judgment of the County Court, who had used the lack of contact between father and children as a factor in allowing the children’s surname to be changed to that of their mother’s. Lord Justice Eveleigh therefore held that —
[The judge in the County Court below] heard that the father had not in fact seen the children for some 3½ years. The children had said that they did not wish to see the father, and they are quite clearly completely identified with the mother. He came to the conclusion that it was in the best interests of the children that they should be known as Ashworth. I myself can see no reason at all to disagree with that conclusion.