True/False if a user is a customer without revealing the actual customer I have a user A and a third party company B. I want to check if A is a customer of B. 


B cannot reveal any information about their customer list to me. 
If A is a customer of B, I do not want B to know which customer they are. They should only know True/False answer to wether they are a customer.


What sort of problem is this? I thought this might be a private set intersection problem but the definition seems to violate my second condition. Is this instead a Zero Knowledge Proof problem?

"Private set intersection (PSI) allows two parties to compute the intersection of their sets without revealing any information about items that are not in the intersection."
A 1-out-of-n Oblivious Transfer protocol would fit as a solution to your problem.

Oblivious Transfer can be viewed as an improved Private information retrieval protocol, because it allows that only exactly 1 item is retrieved from the database, without sharing any additional info about the database. In addition the "sharer" of the database ($B$) doesn't learn about which item ($A$) was retrieved.

If $A$ is not a customer of $B$ then $B$ should only return information in a way to make it clear to you that $A$ indeed is not a customer and not any information  more should be disclosed by $B$.

Tung Chou and Claudio Orlandi have designed a relatively easy to understand 1-out-of-n OT-protocol, appropriately named The Simplest Protocol for Oblivious Transfer. The math used for this protocol is almost the same that is also used for Diffie-Hellman key exchange.

If you really want a computationally efficient protocol, then the OT-protocol designed by 
Moni Naor and Benny Pinkas (Computationally Secure Oblivious Transfer) is more appropriate.