You can only start a conversation with someone who follows you. But Twitter isn’t just a place for individuals only – brands, companies, celebrities, or communities are all on the social network too. That’s why Twitter allows you to customize the options for direct messages, letting you receive messages from anyone, which is colloquially known as open Direct Messages.
How to Allow or Prevent Twitter Direct Messages From Anyone For iOS
Open the app, and tap the last tab titled Me.
Hit the gear icon next to your profile picture, and choose Settings.
From there, head to Privacy and safety.
Find the option that reads Receive Direct Messages from anyone.
Turn on the toggle to receive messages from anyone, or turn it off to limit messages to followers.