I don't want to keep going on about the crappy name, but there are still some wild cat names left, which haven't been used.
Cougar
Lynx
Wildcat
Bobcat
Margay
Asiatic Lion
to name a few...
The OS X names were specifically big cats, not "wild cats". Here is the Wikipedia definition:
The term big cat, while not a biological classification, is used informally to distinguish the larger felid species from smaller ones. One definition of "big cat" includes the four members of the genus Panthera: the tiger, lion, jaguar, and leopard. Members of this genus are the only cats able to roar. A more expansive definition of "big cat" also includes the cougar, cheetah, snow leopard, and clouded leopard.
They had already well and truly used all these names - in fact they had duplicates (except clouded leopard).
* A "panther" refers to leopard in Africa and Asia, a cougar in North America and a jaguar in South America.
* Puma and mountain lion already refer to exactly the same animal - Puma concolor - and cougar and panther are other names names for this species.
My guess is they shied away from "Cougar" due to it's other connotations and went with "Mountain Lion" instead.