It’s possible to automatically share your name and photo with contacts in Messages, so they’ll know who are you without having to manually add your details to Contacts.
To do so, go to Settings > Messages > Share Name & Photo and flick the toggle to the on position. Now select whether you want to automatically share your name and photo with contacts, or if you want to be asked every time.
Fill in your First name and Last name in the fields below your image, and tap Edit under the photo if you want to select a new one (either from Photos or your Animoji collection).
Now people you message for the first time will see your name and photo instead of just your phone number.