Apple has not really changed the notification sound on iPhone since iOS 7. So how will you hear strange pings, plunks and doots coming from your iOS device? No, it's not an app you downloaded (although third-party apps may have their own messaging sounds). Instead, what you're experiencing is probably the result of updating your iPhone to iOS 13.
The latest iOS update comes with over 200 new features, not to mention over 20 additional changes that iOS 13.1 brings to the table. Among these changes is a new suite of audio for Tapback, an iMessage feature that was introduced in iOS 10. If you don't know Tapback by name, you know it from experience ̵1; they are response options available in Messages about Love, Like, Dislike, Laugh , emphasize and ask.
Previously, Tapback messages would use the same message sound as your other messages, and would even arrive silent when in chat. With iOS 13, however, each Tapback has its own, unique warning tone. What you hear is the tripping of someone who "loves" your message, "boing" a "question" reaction, or any of the other four new reaction warnings. Apple uses these sounds both in chat and throughout iOS, so you can quickly distinguish between a real message and a simple Tapback response.
If you're not a fan of these new sounds, tough luck. It is true that Apple does not include a way to customize the alert tones for Tapback, nor does it provide an option to turn them off completely. If you do not want to hear Tapback, you must disable audio for all message notifications, which is a bit much if you ask me.
A less drastic measure? Just mute your iPhone with the switch off.