What's the name of that golden bird mount?

[Aster_E]

That's the Firebird. It was made available at the end of Heavensward. You need to get all 7 birds from the extreme versions of the trials. Bismarck, Ravana, Thordan, Sephirot, Nidhogg, Sophia, and Zurvan. Once you have all 7 birds you can accept the quest for the Firebird in Idyllshire.

I think you're talking about the Firebird mount.

You get it from obtaining each of the Heavensward Extreme primal bird mounts.

They are both totally wrong, and it is actually the Firebird, which you get from a quest that opens in Idyllshire upon acquiring all seven HW extreme primal mounts. [/SARCASM]