Website hosting companies tend to need your real name, real address, and real billing info to verify those things are correct. Isnt Medium more private, because you don’t need to feed it any of that?

No, if you know where to look. Medium is just awful. There are too many things wrong with Medium that I won’t elaborate here, but I’ll leave some sources:

• https://tosdr.org/en/service/1003
• https://nomedium.dev/
• https://www.cdevn.com/why-medium-actually-sucks/

The alternatives that I recommend on my comment have decent privacy policies and are not even close as an abuser as Medium is. They are also free software.

Here there are some decent server providers recommendations for self-hosters which require nor your real name or billing address in case anyone is interested.

https://privacy.awiki.org/#hosting