To be "[name] Junior", you must have the same name as one of your parents.
How does this work with things like "[name] the Third"? Do you have to be the third in a consecutive line of [name]s, or can there be other people in between?
How do middle names fit in to all of this? If Michael James has a son named Michael John, is Michael John not a 'junior' because the middle name is different, or does it only go by first names?