I lost my AirPods at school

I lost my AirPods at school. They were named Sophie’s AirPods. A day later I found my missing AirPods, and I connected them to my phone, and it said Sophie’s AirPods. Are they for sure mine if they said that when I connect them to my phone. Also, if the AirPods were not mine, would it have said “Not your AirPods”?

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