Answer:
A man with the same name as his father remains a Jr. his son would be III. II is only used for naming a son after ANOTHER family member such as an uncle or grandfather and ONLY when all names are exactly the same (FIRST MIDDLE LAST).
A Junior never becomes a II. Try explaining "it's automatic" to the Soc Sec Admin, IRS, your employer, and countless others who have legal documents with your Jr. on record.
I guess you could LEGALLY change your suffix from Junior to II but why?!?! It is not consistent with genealogical nor historical precedent.