On where the name id came from:
According to David Kushner's Masters of Doom, p.31 --John Romero and Lane Roathe combined their one man companies into "Ideas From the Deep."
p.57 -- when they made "Dangerous Dave in Copyright Infringement" they used the name "Ideas From the Deep."
p.77 -- when they left to form their own company they shortened "Ideas From the Deep" to "id" for "in demand." It is said that they didn't mind that "id" also stood for "the part of the brain that operates on teh pleasure principal."
There are also a couple of other mentions of "Ideas From the Deep" elsewhere in the book. So, at least according to that book, id WAS a shortening of Ideas From the Deep.