Can PayPal payments be sent without revealing the sender’s name?

No you cannot.

Anonymity in payments is frowned upon and all participating banks, payment institutions, and e-money institutions make it a point to adhere to the travel rule per se, which is that the sender’s identity and information are passed along. This is more so true now in the crypto world and post FACTA guidelines for crypto that cam out, that basically says, your name will travel along for the payment, whether it is PayPal or not.