Simply a junior.

"A man who is a "junior" usually stops using Jr. upon his father's death. If he is married, his widowed mother uses "senior" to distinguish herself from her daughter-in-law. "Senior" should be spelled out using lowercase s. It may be abbreviated to "Sr." when used with an especially long name." The same goes for junior, as in Mr. David Smith junior. However, if senior was a well know public figure, junior continues to use the title to distinguish himself in order to avoid confusion.

The use of "junior" versus "II" or "III" can also be of interest to some of my clients. While many think that those are interchangeable, according to etiquette, they are not. There is one slight difference. " 'Junior' is used by a man whose father has the same name that he has, whereas the "II" is used by a man who has the same name as the older relative (... grandfather, [great grandfather, uncle]) other than the father." A comma is used to separate a name and "II" designation. Some man dont like to use a comma. Either way it is proper - just personal preference.

{The Wedding Blue Book by Crane & Co.}