The fourth example was studied by Brady and Crisp in their CMH paper CAT(0) and CAT(-1) dimensions of torsion-free hyperbolic groups, so it would be reasonable to call its fundamental group the "Brady--Crisp group". (Brady and Crisp also note that it belongs to a family studied by Haglund and Ballmann--Brin.)
They study a one-parameter family of CAT(0) metrics on the complex, and prove the very nice fact that any CAT(-1) model for this group has to have dimension at least 3.