This article explains how to select custom tones for text messages on iOS 12 and later. The steps also apply to earlier versions of Apple's mobile operating system, but may vary slightly.
How to Change Your iPhone's Notification Sounds
Every iPhone comes pre-installed with dozens of text message tones. You can set one as your iPhone's default text message tone. Then, the text message tone will play every time you receive a text message. To change the default text message tone on an iPhone, follow these steps:
From your iPhone's home screen, tap the Settings app.
Tap Sounds & Haptics (or Sounds in some older versions).