this is for the wookie hunter mando clan right? I don't think they'd use a technical name other than At-St, because essentially it is a re-purposed at-st correct? The just took the existing vehicle and customized it into a wookie-hunter (btw you do realize that there is an established "wookie hunter" at-st already created in the expanded universe? it has big giant gun "arms" on each side!)
so... I'd call it something wookie related or something like a pet name for it (kinda liked leggy, that's great)
they could call it their "adenn ad'ika" or merciless darling
Source for mando words from wookipeedia:
adenn (pl. adennate) - merciless
ad'ika - kid, lad, boy, sweetie, darling, son, daughter, child