Retains its original name after taming. You should try to tame Gorgonite as quickly as you can, before a Son of Gorgonite appears and tries to 'help' you by attacking it.
Level scaling: In Shadowlands most NPCs will scale with the Hunter's level, within the constraints of their level range. Hunters can tame regular NPCs up to 2 levels higher than them, but can only tame elite NPCs of the hunter's level or below.