How to hide computations from client side on the web

I need guidance on how I should go about building a website and what libraries and services I should use to accomplish it.

Basically, information of who is logged in is presented on this website. When you enter the site you can see a list of people who are logged in with a random number by their name. To get on the list, you can log in yourself. When you log in, your name is sent to a database (maybe firebase?). Then a random number is generated (based on the length of name string) on the server side and stored in the database too. The database refreshes and the name is added on the site.

What I need help with: I don't know how to send information so I can do computations or execute code where the user can't see. Maybe AWS? But I'm still not sure how to pass information to an AWS server.

How should I go about this?

Thanks!