A distinct sound means you don't have to check your phone every time
Giving an important contact or a busy group a sound you can recognize without looking means you can tell at a glance whether a notification is worth interrupting what you're doing for.
Not every app supports a fully custom sound per chat
How granular this gets varies by app -- some let you assign a unique sound to any single conversation, while others only offer a handful of preset tones or limit customization to muting rather than a distinct sound per chat. If your app doesn't support per-chat sounds, setting a custom ringtone for that person at the phone's contact level is a reasonable workaround.
Frequently Asked Questions
Can I use my own sound file as a notification tone?
Many phones let you pick any sound file saved on the device, not just the app's built-in options, though this depends on your phone's operating system as much as the app itself.
I changed the sound but it is not working -- why?
This is usually a caching issue. Fully closing the app (not just backgrounding it) and reopening it typically applies the new setting correctly.