If we don't want the Kingdoms to have names based on real words, we can just make them sound cool:
West: Varafels - The well known 'Bitter Sands'. When one thinks of the Hueco Mundo, they usually truly think of Varafels - constant fighting between hollows and arrancar, sprawling underground caverns, packs of hollows with tyrants at the helm, the feudal society that drives their world...it is encapsulated neatly in Varafels. The Bitter Sands are a place of constant fighting and bloodshed, and it is here that the former Espada, now Simetria, choose to stand their ground and bring order...
North: Imhuvlt - although most hollows and arrancar refer to it more commonly as the 'Silent Sands'. Characterised by the shrouded moon and absence of wind. Formerly ruled by Graven Fel, in simpler times - Imhuvlt is host to more ancient ruins than any other Kingdom, where arrancar and hollows set up bands before the rise of Nox Xorik. Now, the Kingdom is united in fear, has built a reputation for sin and depravity, and it is building new, more terrible structures than once before...
East: Ceurormir - the one hope of Hueco Mundo, the 'Blessed Sands'. Once, the weak flocked to this region to escape the chaos of the land and the tyranny of the strong, and they built something that didn't fall. Ceurormir is the place of true civilisation in Hueco Mundo, and although it was conquered by one of the Kings, their rule was benevolent enough. Now the people have a Queen, glorious and radiant, and much of the Kingdom would do anything to see her will done...
South: Kerriax - also known as the 'Shifting Sands'. Kerriax is geologically unstable, the ground cracking and the threat of quakes ever present. This has led to most of the hollow colonies being buried, and as such the hollows here make their lives on the surface. The area surrounding the former King Karasu's Castle is stable, and thus it has been a hub of this Kingdom, with hollows flocking to it's gates daily. With the death of the King, the Kingdom shall surely fall to ruin...