Logout?

Players are only allowed one account: https://support.chess.com/customer/en/portal/articles/1444776-can-i-have-multiple-accounts-

However, if your device is being shared or you just need to log out, you can find it under Home > Log Out on the website menu and under Settings > Logout on the app.

Ty Martin. In your link I found is forbidden why to have two accounts is considered a type of cheating. In my case I  would like my grand son, aged 8 years, can play with his account using my iPad. I saw in the website it is possible to logout and change account, but why it is not possible in my iPad from the dedicated App? 

You should be able to from the app. I'm on Android and it is in Settings. You actually have to scroll down to the bottom to see it most likely.

There is no X

No X where?

There is no way to logout of the iPad app.  It is impossible to sallow my son to use my iPad with his own Diamond membership.  How silly.

Unlike Android tablets and phones, iPads and iPhones were not designed to be used as a shared device.

However, are you using your Apple ID to sign into Chesscom? Does your son have his own Apple ID? You could try to sign out your Apple ID on your iPad and have your son sign in with his Apple ID on your iPad. He then should be able to login to Chesscom with his Apple ID. But be aware, like I said,  iPads (and their apps) were not designed to be used as a shared device.

Look in the Settings menu for the logout. As far as I'm aware you can log out and use am account name and password on iOS. Not sure if you can use multiple Apple IDs.