There are some founders who are aware that their early employees are invested in the financial security of the company, and not only aren't scared of these questions, but openly discuss company finances.
Asking them to name the bank is a bit of a weird one, only because the answer can't be SVB anymore, and I'm not sure what OP would do with that information. (So it's FRB, then what? Unless you have inside info that they're about to fail, and you're interviewing this week, I don't see how their banking partner's material) But if a startup you're interviewing at won't answer what their runway is, or the rest of the reverse interview business questions, then that's a red flag and you should run far, far away from them.
* Are you profitable?
* If not, how long is your runway?
* Where does the funding come from and who influences the high level plan/direction?
* How do you make money?
* What's preventing you from making more money?
* What is the company's growth plan for the next 1 year? 5 years?
* What are the big challenges you see coming up?
* What have you identified as your competitive advantage?
