The existing Clan 'Mechs, Omnis or standard, have wide variety of names and no consistent themes. The Clan Wolf uses "wolf" in several designs but at the same time they have many 'Mechs that don't refer to wolves (Woodsman, Arctic Wolf, Timber Wolf, Gargoyle, Linebacker, go figure). The Ghost Bears are fond of bears in names but again, this is not consistent. Likewise with the Smoke Jaguars and Nova Cats referring to cats.
Still, overall it looks like most Clan 'Mech names refer to animals. Makes sense, given their tribal bent and their totems, though the names aren't necessarily assigned to units that would exhibit traits of their namesake (for example, the Kingfisher). They often use normal animal names, with Homeworld's modified animals being seemingly non-existent, the Nova Cat being an exception (unless i missed something else). Presumably Clan totems shouldn't really be enshrined as 'Mechs, the Blood Spirits certainly didn't like the Star Adders naming a 'Mech Blood Asp (directed as an insult).
Rest of the names have no consistent pattern whatsoever. There are some descriptive ones (Bowman, Skinwalker), some swords and other weapons (Flamberge, Wakazashi, Tomahawk), mythological things (Hades, Jupiter), hunting (Woodsman, Huntsman), basically random words (Linebacker, Pouncer), re-used Star League names (IIC-design)...
Oddly, the Clans favor various gods, especially war gods, for their combat vehicles. Quite ironic, given how they basically venerate 'Mechs as god-like things for warfare.
So, chances are new Clan 'Mechs are named after animals, but if not, it is likely to be something war or aggression related.