Then lease your VPS. And if it really matters, you can daisy chain VPS via Tor .onion SSH.
Simply exchange them to Monero. If you want, mix them, but only a single pass is needed. A mixer is a trusted 3rd-party, which introduces serious counterparty risk, and vulnerable to multiple forms to input-output correlation attacks, in the worst case, provides no security.
If you are paranoid, create multiple Monero wallets, and send the funds back and forth, each time with a randint(1, 100) hours delay to frustrate timing analysis. Please note that you should only run full node Monero, and must run it inside Whonix, otherwise, the unencrypted Monero traffic is exposed. The situation of P2P-level encryption of the entire cryptocurrency world is a disaster, almost all traffic is clear.
Ring-CT is possibly not the best cryptographic implementation of transaction anonymity, but currently the best practical implementation available. CoinJoin is a P2P version of mixer, but has no wide deployment, zn-SNARKs involves cutting-edge cryptography and provides 80-bit security (read, not confident), but 90% of Zcash transactions are clear transactions, makes private transactions vulnerable.
Or, once GNU/Taler is available, making an anonymous payment would be as easy as using PayPal.
... With a credit card (which of course has your name on it), since AFAIK the providers tend to only accept bitcoin for established accounts.
Cockbox (Bitcoin and Monero) at https://cockbox.org/
HostSailor (cards, transfers, Bitcoin, etc) at https://hostsailor.com/
Trilight Zone (cards, transfers, Bitcoin, etc) at https://www.trilightzone.org/
VPS.BG (PayPal, Bitcoin, etc) at https://www.vps.bg/en