In the UK there's actually no requirement to register a child's birth using the surname of either parent.
So, for example, John Smith and Mary Jones can legally register their son's birth calling him Peter Bloggs. When they have another child later on, they can register her birth as that of Doris Havers.
It's only convention which dictates that the surname of a parent (usually the father) will be given to a child, not law.
Further, as long as they're not seeking to defraud anyone by doing so, anyone in this country can use whatever name they want, whenever they want. So, for example, someone whose birth certificate names them as 'Colin Parsons' can legally call himself 'Michael Harris' in the morning, 'Sister Agatha Brown' in the afternoon and 'Universal Leader' in the evening. He's fully entitled to sign legal documents (such as contracts) using those names; he doesn't require a deed poll to do so.