Zirakzigil is the Silvertine, and apparently "zigil" means "silver", so "zirak" presumably means "tine" i.e. "point" or "prong".
http://tolkiengateway.net/wiki/Zirak
Barazinbar is the Redhorn, and "baraz" means "red, so "inbar" presumably means "horn".
http://tolkiengateway.net/wiki/Barazinbar
So "Zirakinbar" seems to mean "point (of) horn", maybe referring to the tower's appearance, like a sharply projecting spike on the mountaintop?