Having the same name as the rest of the family
The courts don’t give much weight to “reasons given for changing or seeking to change a child’s name based on the fact that the child’s name is or is not the same as the parent making the application” as summarised by Lady Justice Butler-Sloss in Re W, Re A, Re B (Change of Name)  EWCA Civ 2030.
For example, in Re WG (1976) 6 Fam. Law 210, it was put forward as an argument that it would be more convenient for the child’s school, and that it offered greater security, for the child to be known as the same surname as her mother. Lord Justice Cairns rejected this argument, holding that —
While I have no doubt that there is administrative convenience from the schools point of view in having the child with the same surname as the people with whom she is living, I really cannot see that this suggestion of greater security can be of any substantial force. There must be, after all, thousands of cases in which children are living with foster parents, or with maternal grandparents, or uncles and aunts or other relatives, who have a different name from the name of the child. Moreover I think it is wrong to attach too much importance to considerations arising in connection with schooling as against the longer term interests of the child.
Neither does the fact of the mother re-marrying another man add any extra weight to the argument, or the fact that she has custody of the child. Later, in the same case, Lord Justice Cairns held that —
… the mere fact that there has been a divorce, that the mother has remarried and has custody of the child and has a name different from that of the child, is not a sufficient reason for changing that child’s surname.
Mr Justice Wilson, in Re B (Minors) (Change of Surname)  1 FLR 791, came to the same conclusion —
In these days of such frequent divorce and re-marriage, of such frequent cohabitation outside marriage, and indeed increasingly of preservation of different surnames even without marriage, there is, in my view, no opprobrium nowadays upon a child who carries a surname different from that of the adults in his home. That view is supported by a comment of Ralph Gibson, LJ in Re F (Children: Surname)  1 FCR 110 at p. 114E.