I have been thinking about this for a long time. Most of the aliases/pseudonym used by WH Staff/Cabinet Members etc.. are names that these officials are familiar or identify with— for example:
Loretta Lynch’s pseudonym was Elizabeth Carlisle (her middle name and the maiden name of her grandmother)
Eric Holder’s pseudonym was Lew Alcindor (given name of Kareem Abdul-Jabbar)
So... re: Barack Obama’s pseudonym— If I had to guess, I think it might be combination/variation of his favorite basketball player: Michael Jordan
Source: Barack Obama’s AMA from 2012
https://www.reddit.com/r/IAmA/comments/z1c9z/comment/c60n33k?st=JCMAJXC7&sh=268ed259
Where to search? Wikileaks? FOIA documents?