Chances are, the Alert Sound chosen by your daughter is Glass. Settings > Sound & Haptics > Text Tone > Classic > [See the list below].
Here are the iPhone text tones (under Settings → Sounds & Haptics → Text Tone) that have discrete bell-like “ting” sounds with a natural fade:
- Glass – very clear, high-pitched “ting” with a nice decay.
- Note – softer, bell-like pluck with fading.
- Pulse – short separated “ping-ping” with fading resonance.
- Chime – gentle bell chime that rings out distinctly.
- Keys – higher-pitched, discrete ting-ting with quick decay.
Those are the main ones that sound like individual bells rather than continuous tones or synthetic beeps.
Based on your “ting… ting… ting (fading each time)” description, Glass and Chime are the closest suspects.