Caesonia was Caligula's last wife, and her name comes from the Roman gens name of "Caesonius". The meaning is perhaps lost in antiquity, but the name may have been derived from the Latin words *caesio* ("the cutting or lopping of trees"), *caesor* ("one who hews something"), *caesius* ("blue-grey" in reference to eye color), or (most likely of all) *Caesonis* -- the genitive form of the praenomen "Caeso", literally meaning "belonging to Caeso".
And, judging from the abrupt imperiousness of your command ("Find a meaning to my name") I see you are aptly named. ;)
Oh, and you're welcome.
-- Nanaea