True and you did say there was a younger son named Elias.
However I have seen Joseph Elias Carroll, Jr. which confuses those who think that the father must be Joseph Elias Carroll as well which is not mandatory.
Two other possibilities and still we have a man sure his name should be Joseph Elias Carroll, Jr.:
(1) His father is Joseph Carroll, nothing more.
(2) His father is Joseph Elzebub Carroll or
Joseph Eloysius (a variant of the other one) Carroll or
Joseph Eliakim Carroll and so forth;
where in (2) there was a desire to change to a less weird middle name but still be one of Biblical appearance and (1) where the son's descendants, and possibly the son himself, saw him as his father's namesake, which indeed was, and thus Junior was used where some thought it required a complete match, and it does not truly so require at least as done in practice.
On the other matter, it will be hard to document completely any claim to nobility here, but we Wylies have the same for our American matriarch, being a disinherited daughter of rich nobility for marrying a physician Covenanter or whatever, which has yet to be even personified with her father's name, much less full documentation.
"As yet undocumented family lore" or similar honest honorable phrase is the best way to keep it, not dismiss it, but not be a shill to something that just is not yet known.