Suitov Iceheart is known to refer to this world as 'The Loom' or 'Loomworld'. That isn't an official, or even preferred, name for the place. He seems to do it mainly to be annoying.
One of the leading powers at the time of the Great War is Weft's home city-state, whose name (according to Weft) is translated as the Whitish City. ('Off-White City' is better. 'City the colour of unbleached (insect) silk', is a good if unwieldy compromise; whereas 'Ivory City'... might give people dippy ideas.)
The Whitish City is the only weftworld humanoid civilisation we have heard about. We know that Weft's monastic order numbers among its institutions, that there are two social classes ('aristocracy' and 'working class') with very rigid boundaries between, that the state has a fairly high degree of involvement in people's everyday lives, and that gods and divinities do, at least to some extent, really exist there (Weft and his brethren have even been hired by them, or hired to negotiate with them, in the past). (See Weft's pantheon.)
Related topics
Games and pastimes on Weftworld