i maintain that the principal issue with choice (a) is unrelated to the "with" issue. instead, the primary problem with (a) lies in its meaning.

* According to the sentence, the companies are intentionally avoiding the use of "A", "B", "1", "2", etc. So, common sense dictates that they're aware of the reason; they are certainly not avoiding those labels at random!

the problem with (a) is that it says only that companies are aware "that there are connotations". in other words, literally, the companies just know that there are connotations -- in other words, that connotations (of some sort) exist -- but the companies don't necessarily know what those connotations are.
the correct answer, on the other hand, explicitly states that the companies are "aware of the connotations" -- i.e., aware of the actual nature of those connotations.

analogy:
i am aware that discounts are available this weekend.
--> i know that there ARE discounts, but i don't necessarily know the specifics.
i am aware of the discounts available this weekend.
--> i actually know the specifics (percentages or whatever) of the discounts.

* (A), (C), and (E) don't deliver the intended meaning.
I.e., these choices don't actually say that the companies know what the connotations are. It just says that the companies know "that there are connotations".
This is a HUGE difference. If the distinction is not immediately obvious to you, consider the following sentences:
1/ I know that there are passwords for all of your bank accounts.
2/ I know the passwords for all of your bank accounts.