Cultivar Epithets, and Orchid Names

[zxyqu]

I'm hoping this is the right place to ask this, but could also fall into Advanced discussion I guess, but here goes.
If you get a seedling cross, and it's unbloomed and unnamed other than the parentage, who, and how can name the eventual flower. Obviously all seedlings will be different and deserve their own cultivar name (I mean how many ridiculously awesome Joy Spring Canary's does Peter Lin have right??). Anyway, I picked up a couple of unbloomed seedling crosses, and got to wondering if I could name them, or if that privilege rests with the nursery who crossed it.