I searched further to find out the proper use of the suffix “II”. It
seems that this is used primarily when the child has the exact name of
another relative, but not his father, or when there are three family
members (father/son/grandson) with the same name:
“The designation of Sr. or Jr. to distinguish between father and son
with all the exact same names (first, middle, & last), can be replaced
by the Roman numerals, I and II, respectively, when the grandson has
the exact same names. The grandson will then have a III after his
name. The grandfather and father can continue to use Sr. and Jr.,
respectively, or the numerals.
“However, using the “II” (not Jr.) often means a man does not have his
father’s name, but another relative such as his grandfather or uncle.
“Of course, royalty or other ceremonial title, would always have the I
or II, rather than Sr. or Jr. to designate the line.”
I don’t know about that theory about the use of II, instead of Jr.
We used II for my son, instead of Jr. because his grandfather hated being a Junior at seventy years old.