Layne Staley did go with Alice N' Chains when he and Jerry Cantrell started the band in Seattle in 1987, but they soon changed the name formally to " Alice In Chains," and in fact their third album ( 1995) is titled, " Alice In Chains." ( Obviously, using either will very probably mean the listener knows you're talking about one of Seattle's 4 great grunge bands.)
Soundgarden was closest to PJ, given the collaboration of the late and I do mean great Chris Cornell and Matt Cameron with Jeff and Stone on " Temple of The Dog," to honor Chris' roommate and Jeff and Stone's band mate Andrew Wood who had died of a heroin overdose just as Mother Love Bone released their first and only album, and "Temple of The Dog" also brought Eddie Vedder and Mike McCready into the picture to work on the TOD album. A pretty good argument can be made that if Andrew Wood hadn't OD'd, there would have been no PJ, who were originally " Mookie Blaylock," named after their favorite Seattle Supersonics' player but also already the name of a really good black jazz pianist
, thus " Mookie Blaylock" became Pearl Jam.
