The family name drop feel like a red herring. He know he is going to die. It's one thing if he got some sort of self destruction type stuff so he could do the cliche 'let me tell you who kill you', but he doesn't, so it's just one side info drop. Dropping a name of a likely enemy force them to make assumption & left likely to put in as much effort to fact check as should be.
Or he is just really stupid & said the name of the family he work for.