I have this same experience. So far I have noticed this addition of false or true names only on North Carolina's death certificates. Ancestry has not provided any supporting documents to confirm why they determined the name on or not on the death certificate is false or true. Ironically, the citation sources are ancestry records or personal records which confirm the name shown as a false name is actually a true name. I reported this via phone regarding search and records. Hopefully Ancestry will drop this information from their death certificate citation source.