The iPhone’s notification sound is iconic at this point. While you've had the option to change the alert sound for notifications like messages, incoming emails, and reminders, as well as certain third-party apps, Apple never let us change the default alert sound for other notifications. That chime is arguably almost as strong as the iPhone brand itself, much like the Windows XP Bliss wallpaper or the Mac boot up sound.
In any case, Apple finally letting go of that legacy, and we’re all better for it. In the fourth public beta for iOS 17.2, Apple added a brand new section for changing the default alerts sound. While the feature is currently in testing, the iOS 17.2 should be available for the general audience in a matter of weeks. If you’re curious, you can install the public beta, without even installing a new profile.
Once your iPhone is updated, go to Settings > Sounds & Haptics to find the brand new Default Alerts at the bottom of the list. Here, you can change the sound to any of the text tones, new or classic.
While you’re here, you might also want to change the default haptic feedback. iOS 17 changed the haptic alerts, and there was no way to go back. With the iOS 17.2 update, Apple is letting you customize the haptics as well, so you can go back to how it used to be, or choose the haptic feedback level that works best for you.