Reading through this thread and remembering my babka I remember how she would never call me my English name, Rebecca and only call me the Russian equivalent "Rivka", ha.
I think Rivka is really pretty, but Russian names are often pretty but kind of fascinating too. They tend to have variations that are "equal" to their real name... according to Russian friends of mine at least. Like Natasha who is also called Natalia, which to me are two different names but to her is the same... fascinating. Maybe your babka thought Rebecca/Rivka was essentially the same? 🙂
Both of my dogs are Russian by the way, but only one of them has her original name (Fanja).
Bexray
It's pretty but it really annoyed my mum!