In relation to the ex-CEO of Sony, he writes it as 出井 (出 as in 'depart, go out', and 井 as in 'well'), another possiblity would be 出射 (射 is found in verbs 'to shine', '射す' and 'to shoot', 射る).
Written as Idei there is no meaning (it is not an actual word in Japanese). Because of the way Japanese names work if you said Idei it wouldn't be clear that you meant to write it 出井 and if you wrote 出井 it wouldn't be clear the reading was supposed to be Idei (it could just as well be read, as a last name, Izui). This is why pretty much all Japanese forms come with two spaces for names - one for the kanji, one for the kana that explain how the name is read.