On the envelope in which a death certificate is issued, it says,
"The registrar will ask for the following information about the deceased:
- date and place of death and usual address
- full names and surname (and maiden name if the deceased was a woman who had married)
- date and place of birth "
(plus a couple of other things not related to name)
You are not required to produce certificates to back up the names given.
So if someone adopted a different name from their birth name and was generally known by it, to the point that it appeared on their medical records and hence their death certificate, and if that name was given to the registrar - there would be no requirement to prove that the name was changed through marraige.
The death would therefore be registered in the name given to the registrar, who would not question that unless there were obvious discrepancies (eg the certificate showing one thing and the registrant saying something else!)