This is what a New Hampshire *should* look like.
Hatcheries really do not breed to standard - I have some hatchery NH and they don't really look like that LOL
As for an abbreviation for Hoover's Rainbow...I suppose you could make one up :)
https://insteading.com/chickens/breeds/new-hampshire/
If they are Rainbow pullets from TSC then very likely they came from Hoover's Hatchery. They would be a mixed breed and not New Hamphire. While coloring is similar, alas, they are not NH - but you can call them what you like if you are keeping and breeding them for your own use. I just would...
If you can get some photos that may be helpful.
Where did the chickens come from?
From your description I would suspect you are talking about the "Cushion" of the chicken.
I have one New Hampshire (Hatchery quality) that has a fairly pronounced cushion, another that you can tell it's not...