BABY = Black And Blue Yearbook, aka the SR3 Limited Edition book.
We already had two different BBB's (Big Blue Book, aka SR1st Ed, and Big Black Book, aka SR2nd Ed), so we needed a new name for it. And the year it came out, a TON of us from the ShadowRN message boards either went to Gen Con, or sent money to someone to pick them up a copy (I picked up *10* copies of the damn thing for folks in Canada, England, Germany, and Australia). A lot of folks that year (and over the next couple years) used the books to get signatures from SR artists, authors, and anyone else who worked at FASA at the time, as well as fellow Shadowrunners and friends. It was, in essence, like a High School Yearbook for us. Hence the name.