[mirimir]

Sure. But each VPS has its own IP address. The VPS provider probably retains logs. And its ISP probably also retains logs. And everything involving that IP address is associated with you.

[dvcrn]

For incoming traffic yes, but outgoing traffic is heavily dependent on what you use. A lot of virtual spaces use the same outgoing IP

[mirimir]

I don't recall seeing that. VPS got their own public IPs. Which would show up in ipchicken or whatever.