I'd say it depends on the send. In the end paynyms are nothing but a collection of addresses. If you sent the a full UTXO from an address corresponding to paynym1 to an address corresponding to paynym2, it will still be labeled by surveillance companies as a self-spend. If you send from KYC exchange straight to Sparrow, then from Sparrow to Samourai, it will still be pretty easy to follow the coins. The privacy benefits of Paynyms per se are elsewhere (mainly not reusing addresses). Coinjoin is a much more useful tool for what you're trying to do.