What this screen is
Your public profile - what somebody who is not signed in sees when they follow a link from a draw or a table.
Switching it off
You do not have to have one. Turn it off and the page is not found rather than empty: a page that said "this player has hidden their profile" would tell a stranger you exist and where you play.
What is never on it
Your phone number and your email address, whatever your settings say. They are simply never put on the page, so there is nothing to get wrong.
What you choose
Your record, your rating and your club can each be shown or not. Changing any of them takes effect immediately.
Your own data
Everything this application holds about you can be downloaded from Privacy in your account menu, and you can ask for it to be deleted there too.