How to unlink someone else's Icloud account from my icloud

This is a mess. Unfortunately the phone was not properly prepared for a new owner, and when you signed in you probably did not tell it to erase content. That resulted in his content being mixed with yours. This is what should have been done What to do before you sell, give away, or trade in your iPhone or iPad - Apple Support

The notifications are probably from apps he downloaded with his account and now require the phone be signed in with his account to update. Delete those apps and download them with your own account. If you have a mixture of apps from two accounts you will have to manually update them one by one and see which ones ask for a different account.

His iCloud account may still show up in Find My. If it does then he will have to remove it. Eventually you may do something that will absolutely require his information to unlock the phone. If you cannot remove it you are left with a useless device. See Turn off Find My on your devices and items – Apple Support (UK) Until this is removed then technically the phone still belongs to him and will eventually see you as a thief trying to gain control of the device.