The phone of a new contact showed my name without having me as contact yet

I am using an iPhone 12 Mini, with the latest software updates. Met someone today and we exchanged the contacts, but something funny happened:

1. I gave him my phone to enter his name, phone and email
2. I called him on the number he wrote (my new added contact)
3. My name was displayed on his phone.

How was this possible? I think he uses Android, but I am not sure.

That sounds like basic Caller ID, Its not a new feature, but if you don't want your name showing up on others devices, you can get a private number.

Yes, I forgot territory is also a big factor. In Canada it is name and number and sometimes location the number is based in. Also most current devices have options to keep your name and number private if you want. But the guaranteed way is to go through your carrier.