It’s not possible to hide text messages on every chat app on the iPhone, but many of these apps do have a few related options you can play around with.

To send an Invisible Ink text, Open the Messages app and start a new conversation or tap on an existing one. Type your message as usual, or upload an image to the text field – whatever you want ...

To hide app names on your iPhone's home screen, press and hold on an empty space on the Home Screen until the icons start ...

To test the seemingly hidden ability to instantaneously trade text messages with someone using the iPhone's Notes app, here's what you need to do: Launch the Notes app.