SELECT from wp_users, get Displayname too

You will need to do a JOIN on the users table in your old database, and also select the display name.

One key thing to note here, is that I aliased dbold_posts as P, and dbold_users as U – when dealing with multiple table, it’s always best practice to specify which table you are referring to when mentioning a column.

SELECT   P.post_author, count(P.ID) as amount, U.display_name
FROM     dbold_posts P
JOIN     dbold_users U on U.ID=P.post_author 
WHERE    WEEKOFYEAR( P.post_date ) = WEEKOFYEAR( NOW() )
    AND P.post_status="publish"
    AND P.post_type="post"
GROUP BY P.post_author