I hope your pup gets better. She might just be getting used to her food, surrounding and everything. I hope she feels better soon.
Borzoi do tend to have very delicate tummy and are prone to bloat so be careful as she gets older. They tend to wolf down food.
I've never had a Borzoi but was close to a few of my bosses borzoi. I love the breed. They are so elegant and sweet, playful and caring.
She will be fine. As for a name... I think it should be Angel. She looks like an angel and was sent to you from an angel. Hugs