When they chose to pretty up the name of "Portia" they may have been making making a stretch in defining it as meaning "offering". The actual Latin word for "offering" is "donum" or "sacrificium". The Latin word "portio" *might* be a synonym for "offering", as it literally means "a part, section, division, portion", which presumably could be taken to mean something akin to a "tithe".
Except the word "Portio" is already a feminine noun in Latin. If it was meant to be a female's name, then there would have been no need to further feminize it by changing the "o" ending to an "a".
I'm more inclined to believe that the name "Portia" is derived from the famous Roman gens of "Porcius" -- one notable historic "Porcia" having been the sister of the younger Cato and wife of Lucius Domitius Ahenobarbus, the Imperatorial General in the time of Julius Caesar.