Say two parties agree to an NDA, but the NDA has a special addendum that tells the other party that they cannot reveal real information about the first party (the provider) to anyone, including the general public, media, news outlets, etc. Most NDAs are about keeping some information hidden, but is it legally valid if such information pertains specifically to one's identity and personal characteristics (such as name, location, age, height, physical features, and etc.). Will the party still be under penalty?
In other short words, can an NDA be legally permissible and in effect if it pertains to personal info?
An example could be someone operating in business under a different name (not illegal); someone who would suffer financial loss if a business or general public knew some info about them; or someone who has faced public scrutiny (i.e., false criminal punishment) and cannot, at least in good public image, disclose or have someone disclose their identity outside of private business matters.