Show id's that only contain one kind of name

Here is a table which will help me to explain the question a lot.

    id  | name
    ----|--------------
    1   | John
    1   | John
    1   | Arya
    2   | Tyrion
    2   | Tyrion
    3   | Jamie    
    3   | Cersie

I need to make a SQL query that only shows id 2 because it only contains one kind of name. 1 and 3 will not be shown because they have 2 different names. 1 would have been shown if Arya would have been John, because then 1 would only contain Johns.