All you have to do to change your surname, is to use the name you want to be known by. For example, one set of my great grandparents never married, but my great grandmother used my great-grandfather's surname, registered their children's births as though she was married, and her death was registered in that name. She didn't have to do anything except call herself Mrs --- . Nobody knew that they weren't married.
Nowadays this is a bit more complicated than it used to be: our lives are bound up with form-filling and paperwork, but it is, and always has been perfectly legal to use a different name from the one you were born with, so long as it is not in order to commit fraud.
Spinster is a term which applies only to a woman who is not, and has never been married. A person who is widowed or divorced is supposed to declare that at the time of marrying. However you don't have to produce any proof of your condition, so what you tell the registrar is what will be written.
