Comment by grothoff

The privacy properties for P2P transfers between consumers are identical to those with merchants: the exchange can require the receiver to provide information about themselves, but the payer remains anonymous just like for purchases at a merchant. And yes, it involves spending (burning, if you prefer) the old tokens (we prefer digital coins) and issuing (blindly signing) fresh coins. Afterwards, the fresh digital coins are indistinguishable from those issued during a regular withdrawal from a bank account.