Animoji and Memoji are animated emoji that mimic your facial expressions using your iPhone's forward facing camera. While most adults are probably not going to converse with animated emojis, kids definitely delight in them. Unfortunately only the iPhone X or later, iPad Pro 11-inch or iPad Pro 12.9-inch (3rd generation) can create and send Animoji and Memoji (though any iOS or Android device can receive them).
You can personalize your information in Settings > Messages > Share Name and Photo. From here you have the option to select "Everyone" under the Share Automatically options. You will stop receiving notifications if you select this option, but then your phone will automatically share your name and photo with everyone you text message. This is not recommended.
iPhone users running iOS 13 or later can now add a personalized image and name to their messages. This allows you to control the photo and name others see when you send a text message to another iOS device. However, it is basically a suggestion since the person receiving the text message can choose to either use your image and name or use the image and name they have already assigned to you.
With iOS 12, Apple encroaches on Snapchat's turf with a suite of new stickers and filters for the Messages camera, along with the ability to use Animoji and Memoji on FaceTime calls. While the Messages app has had stickers for some time now, they've been relegated to message threads; now you can paste them on photos you take with the app's camera, a feature that's been available on Snapchat for years and more recently on Instagram and Facebook.