Monero uses ring signatures, stealth addresses, and RingCT to make every transaction private by default. There is no opt-in privacy mode - all XMR transactions are private all the time. This means the blockchain record of your VPS payment cannot be linked to your wallet or to your server by any observer, including chain analysis companies.
Bitcoin's transparent ledger allows chain analysis to link transactions with high confidence when KYC exchange data is available. Monero closes this vector entirely. For hosting customers who want verifiable payment anonymity at the blockchain level, XMR is the correct choice.