"Renaissance" means "re-birth" as anyone who speaks modern French, for example, will be able to tell you - and not "Rene's Essence" - as you've been misled to believe by whatever fantastical sources you've been quoting out of (doubtless LDS sources....)
As for the variation in spellings, it has almost nothing to do with illiteracy (although the great majority of southern Italians were illiterate, as literacy had historically been seen as a threat to the powers that be in Roman Catholic countries, as evidenced by all the historic burnings and executions of "heretics"/scholars who had dared to translate the Scriptures into the vernacular language of the country in question, and who then "diabolically" set out to teach, as Luther had put it, the "milk maid" how to read for herself....)
The difference in spelling is due more likely to a different surname origin, than illiteracy; those bearing the surname "Ierachi" having originally come from the village of Jerache (i.e. a place name), and those being named Ieradi (a alternative form of Ierardi) being the "son of Gerardo" (i.e. a patronymic.)
Hope this helps.
DMI