In the contact profile, when I edit the name, I have the option to:
1 put the one I want.
2 leave it blank so that delta shows the one sent by the user.
Now, in the second option, if this contact is also in my address book then delta, it shows the name sent by the users, only until I click on the plus sign 
, then delta shows again the name that is in my Address book, even after deleting this contact from the address book, Delta seems not to forget.