You can create multiple accounts on Medium. You can use one account to just read stuff aka your main account. You could use your another account just for posting content that you don't want to show your real name. I have a story about it; https://medium.com/menlo-office/how-to-publish-anonymously-on-medium-b719a3b42cf8
You can be the part of the publication and submit them your stories. Also, you don't need to buy Medium membership in order to make money on Medium aka join Medium partner program.