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 customise 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 on Web
Click your profile icon in the top-right, and choose Settings.
In the left-pane, go to Security and privacy.
Scroll down to the bottom, and find the option that reads Receive Direct Messages from anyone.
Check the box to receive messages from anyone, or uncheck it to limit messages from followers.