Some months ago someone asked me about the name that would be on the death certificate of a nun. I wasn’t able to answer it at the time but having done some personal research into nuns who were buried at Broadwater Cemetery I’ve found out the following which might be useful for others.
In the civil records i.e. census, death, and municipal burial registers the given name (normally this would be the birth name) of the nun was used. On the gravestone the religious name of the name was used but sometimes the given name was also recorded.
It is perhaps risky to generalize from specific data but my conclusion would be that on civil records the given name would be used but in relating to the religious order the religious name would be used.
In summary if you are looking for the civil death record of an ancestor who was a nun then search under the given or family name. If you are looking in memorial inscriptions records then search under both names. Of course determining the religious name may not be that easy if you have little details of your ancestor’s life.