Well technically it does. Just not if you buy from coinbase where they need a lot of your personal information plus you'll be most likely buying with a debit/credit card.
If you pay someone for cryptocurrency in cash and they send to a wallet you have set up by yourself there is not really any way to prove that it's yours.
If you pay someone for cryptocurrency in cash and they send to a wallet you have set up by yourself there is not really any way to prove that it's yours.