No, with different a middle name from yours, your fiancee's baby will not technically be a "junior".
Junior and "the second (II)" are not the same thing.
We'd discussed this topic back in February, and if you'd like to read other comments on it, go to this URL:
http://www.behindthename.com/messages/4251.html
And click on each of the responses below.
-- Nanaea