It should be "Junior" (although technically one is only a "Junior" as long as "Senior" is alive) if his father was also "Edward Higgins White", but if he was named after his grandfather, then it's "II" (and even if he named his son "Edward Higgins White III" he's still "Edward Higgins White Jr"); see here: http://emilypost.com/advice/mens-names-and-titles/
The birth certificate said Jr. and I changed it to that but after 1953 he started referring to himself as Edward Higgins White II and our standards state that we should use the name they used at the time. Emily Post is fine but I was asking about our standards, not hers.