This would never occur to me to be an issue! First because I don't get why a name needs to be carried on - it seems a very old-fashioned, class thing ("Why yes, I am from the prestigious Money-Sterling family, we own much land!").
And second, because if people do want to carry on a name, then there's no reason that women should have to change their names to their husband's, or that children should automatically be given their father's surname.
I don't think such deeply patriarchal traditions should really have a place in our supposedly equal society... (Of course if one wants to change their name or give the children their dad's name then that's all cool - but it shouldn't be the rule, you know?)