There’s no modem needed, actually. All of that can be done in software, and you can configure a desktop as a PPPoE client (that’s the protocol your router uses to log into your ISP’s network and receive internet connectivity). Obviously, you’d need to configure that PC as a router for other computers to also share the connection, and running a typical interactive system 24/7 as a router is hideously inefficient in terms of power use.
That is pseudonymity, not anonymity