You can try to impose arbitrary things at people, but people being people will not always be inclined to go with our “whims”. Focusing on content privacy rather anonymity is a more successful strategy.
Its weird to make people call you or put you under a different name on their phones. You can tell people to call you “Smith, Ben” instead of your real name “Smith, John” on their contacts list, but if you tell me years ago to call you that, the immature me will probably put you under the contact name Smith, “Wants to be Called Ben” John.