No, having your dad's first and last name but not his middle name does not automatically make you a Jr.
In the context of name suffixes like "Jr.," it typically refers to a person who shares the exact same name as their father, including the middle name. So, if you have the same first, middle, and last name as your father, you would be considered a Jr.
For example:
Father's Name: John Robert Smith Son's Name: John Robert Smith Jr.
If the son's name was simply "John Smith" or "John Robert Smith II" (indicating a second generation with the same name), without the father's exact full name, then the son would not be referred to as "Jr."