I see no reason to include a DBA name when they are not registered to use one and it is not part of your relationship with the customer. Regardless, I don't really think it makes a lot of difference.
I cannot explain in detail how to complete the form because I do not know if you are using the legacy version or the Form 112. Either way, you only have one customer, the entity. If the entity did have a proper DBA name both forms allow for its use without treating it as a separate person (which it is not).
In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.