No, you can not.
- $B$ does not know anything about $A$.
- You need to know if $A$ is actually called Alice.
Well, that does not work. There is no possible proof that $A$ is actually called Alice. That is unless you verify some other credentials, e.g. an ID card. But trust can not be generated out of nothing. That is simply impossible.
For example, if there is no way to verify a persons name, then no one in the world can decide if he is actually talking to the real Alice or to Eve who is just calling herself Alice.
The question has nothing to do with zero knowledge - that is just impossible in general.