I need to have a photo on my text messages so the receiver knows who is texting them. How do I do that?

I have an iPhone 6 and I'm making good use of the texting option for sending messages. I have noticed that most people who text me have their profile photo st the top of the page and their name appears over the message as well. Mine have neither and I can't find a way to set it up. Can anyone explain in simple terms how I can do this? Thanks! Penjie