IS...
We name a person, i.e. body. We don't name their life or spirit or essence. Therefore they do not need their life, spirit, or essence to retain that name. For instance, when you want to know where someone's burial plot is, you don't go to to the cemetery and ask "where'd y'all put the body formerly known as Widder"? You ask "where'd y'all plant Widder?"
Regardless of status, that bag of meat, bones, etc will remain named. To say "their name WAS" means that it isn't anymore.
Coming soon to CSI Tennessee....
Nobody can identify a body because it has no name anymore.