You can go from LLC Name (Foo, LLC) to Registered Agent Name in 30 seconds. You cannot do the same with Company Name to Bank Account (or from Bank Account to Owner Name).
I also use a registered agent for all my LLCs, but you don't have to. You can totally put your own address down when doing paperwork, and then your home address is open to the world.
> If you are doing business in california, you need to register a california llc
No, you can just register as a foreign LLC [1]. Notably, you do not have to disclose ownership to do business as a foreign, i.e. non-Californian, entity in California.
The requirement for qualifying to do business in a foreign State isn't based on whether you are doing business in said state, rather if the business has a physical presence in said State.
Unfortunately for Californians, if any managing member of an LLC resides in California the state requires the LLC to register as a foreign LLC and pay an $800 per year tax.
Exactly, a bank protects your information by default.
A state business registry does not. Which is why you use / might want a registered agent for your business. But you don't need to do the same thing at the bank (and in fact, I don't think most banks will allow an account without a name and a SSN to tie it back to)