In UK it is easy to change ones name on everything except on a birth certificate. That is impossible. In Phil as in UK it is usual, although in UK not a legal necessity, for a woman to change her name on marriage. Again this will mean she will eventually have all her documentation in her 'new' name, but not her birth certificate. So your daughter having a different name from you cannot matter.
In Spain a woman does not take her husbands name when she marries. All Spanish have two surnames. The first is the first surname of the father the second the first surname of the mother. Thus Mr Gonzales Lopez and Mrs Perez Milan's children will be Gonzales Perez. In a way its surprising that the Spanish way did not prevail in Phil, following their 300 years of being the colonial power.