They do not think that their family name has changed, and in searching cites, we may wish to link them to their past, which suggests pushing Jr, Senior, I, II, III, etc as far from the family name as possible and even dropping it for search preliminary search purposes. Now, since the question of titles was raised, I do hope that, if a CIF does allow titles with names it will do so in some way which allows the titles to be clearly distinguished from names. Better to eschew titles entirely than to add to the confusion. Generational suffixes are difficult enough to disambiguate from names. Titles are even harder.
Consistency is an attribute of good databases.
It is difficult to be consistent with names, but, precisely because the questions raised are difficult, it may be worth a bit more thought.