How do I remove an unknown Apple ID from my iPhone 6?

Where are you seeing the ID? Are you seeing an Activation Lock?

If this is a used device, you need to be able to contact the previous owner to have them log out of iCloud or go to https://www.icloud.com/find/ My Phone and erase the device, then remove it from their account. If you can’t do that, the device is useless. Apple won't unlock it.

Turn off Activation Lock - Apple Support.     

If you are the original owner, contact Apple. Apple can remove the Activation Lock if provided the required paperwork. Either take the device, the original purchase receipt with the serial number, and a photo ID to the nearest Apple Store (if it has reopened)

Genius Bar Reservation and Apple Support Options - Apple.    

or contact Apple ID Support. 

 Apple ID - Official Apple Support.    

Contact Apple for help with Apple ID account security - Apple Support.  (Link doesn’t always load)   

Get Support      Work through the screens to get a chat option. 

Apple Support schedule phone call

https://twitter.com/AppleSupport       People have posted it may take an hour or more to get a response.

You are welcome.