The name "Octavian"

[SOCL]

I would challenge the idea that anyone used any form of an "adoptive-cognomen". The other famous example I can think of is the younger Scipio Africanus, also called Aemilianus for his original family name Aemilius, but there again I don't think he or anyone else ever used the "Aemilianus" name. Rather, I get the impression it too was a later invention, perhaps to create a distinction between the two Scipiones Africani, or as part of a sort of "parrot behavior" where a suggestion becomes accepted fact and thus people assign these adopted names "as fact" retroactively. I haven't done an exhaustive search, but I can't think of a single source that shows that these adoptive-cognomina ever existed except long after the fact... Jona, have you?