If we look at the first line cited by the OP we see that the name of an organisation is used, Hessington Oil (I've capitalised Oil because it is part of a proper noun). In American English — and Suits is an American TV series — organisations and companies are often used in the singular. For example,
- Microsoft is one of the industry leaders in accessibility innovation...
- The Coca-Cola Company has on occasion introduced other cola drinks under the Coke name.
It could be that speaker B believes that "they" refers to a company or an organisation, and as a result uses the singular verb in: “Who is they?”