Set up a Messages Profile
iOS 13 and iPadOS has a new feature that allows you to create a profile for Messages. Essentially, it’s just a name and a photo (or Memoji) that are both shared with people you chat with using iMessage.
You’ll be prompted to set up a profile when you first open Messages after downloading iOS 13 or iPadOS. If you skipped that, you can always set up a profile later by going to Settings > Messages > Share Name and Photo.