The question is mainly about finding a good Latin expression for a company.
Pitkäranta's dictionary suggests opus mercatorium or societas mercatoria.
These feel a bit too heavy for the intended use, and without the adjectives the nouns opus and societas are too broad to be understood as "company".
Of these two societas is better as a standalone translation, but it still doesn't quite work.
The word corpus you suggest is a possibility, but is suffers from similar broadness.
It might work well with an added adjective (like mercatorium), but then the phrase becomes too long to my taste.
As you mention, turba is closer to "mob" or "confusion" than "company".
Unless mockery is intended, I suggest choosing another word.
Instead, I propose using the word firma, which can be seen as the Latin version of the English "firm".
It can be used to refer to a company of some kind in Latin (also according to the aforementioned dictionary) and most importantly, the word is correctly understood by many people with no education in Latin.
Replacing persona with firma should be clear enough for most.
They are also both conveniently feminines, so the adjective grata can stay as it is.
I therefore suggest firma non grata.