Since upgrading to El Capitan "This Mac can’t connect to iCloud because of a problem with name@mac.com"

Can you sign into iCloud with that email address/ID?

From that message it could be that you are not signed in.

Please turn off two-step verification for your Apple ID. Test.

I had similar problem. Turned out my Kaspersky virus software was blocking the initial log in to iCloud. I turned off Kaspersky, then logged in to iCloud without a problem and then turned Kaspersky back on. No problem now.

I'm having the same problem. My iPhone and IPad (both on iOS 9.1) have no problem signing into iCloud etc with my usual apple ID pw. Also, I'm able to access my iCloud setting page via Safari. But after I turned on apple's new two step verification El Capitan keeps bouncing out of iCloud. It keeps asking for my apple ID. When I enter it, the iCloud preferences look "alive" for a few seconds, then all go gray! Hope you have some ideas to help me