As far as England is concerned, provided there is no fraudulent intent you can call yourself what you want. The details on a death certificate are provided by the informant who may know little of the real details including the date of birth that is now included on death certifiactes, so the name will be whatever the person was known as. A divorced woman may revert to her maiden name for example but she may retain her ex husband's name. A woman living with a man but not married to him may take his name. This is less common nowadays but 40 years ago may well have been done for respectability reasons. Hope this does not add to your confusion but may be an explanation when the relevant BMD entry doesn't seem to exist or the details don't match what you expected to find.