How to get rid of an spyware on iPhone 8 called News?
The entry that you see corresponds to Apple's News app. The icon isn't displayed because you don't have the app installed on your iPhone.


  After setting the two-factor authentication system on it earlier this week, a connection attempt has been made by someone else (I've received an authentication code on my second phone when I clearly didn't try to connect in any way).


There is apparently no unintended connection attempt. You appear to have received the verification code from Apple on one of your "other" trusted device (which is expected behavior after turning on Two-factor authentication).


  So first of all is it a spyware? 


No, it isn't a spyware.