Spoilers: I'm going to stick to Basics for a while, even though they contain spoilers...
AKA: no nicknames
Looks: 6'7", blue hair, blue eyes, troll-ogre-demon-elf-goblin.
Family: Younger sister of Erick von Trondheim, relations accordingly. Engaged to marry Hjalmar Stovemuessen, heir to the prominent Stovemuessen ranching family of Gratz, at the base of the Gratz Pass into Trondheim. Hjalmar is brother to Hilde von Gratz, Brendan's wife.
Essentially, Vedanya was raised to marry 'down below' to increase the inter-domain Aristocratic ties for Trondheim. Due to the size differentials, it's easier for the big women to bear children for smaller men, than to marry the men down below. One gets the distinct impression Vedanya has little sense of humor about this.