Using "the" before a company name whose first word is "The" [duplicate]

Is it proper to use "the The..." together in this instance?

No, it is not proper. You'll never say a double preposition out loud like this, and even in writing it will mostly be frowned upon except in the most pedantic of settings (honestly, only lawyer documents come to mind).

It's even better if you rephrase your statements to avoid this entirely. Consider the following:

  1. Under The Red Room Code of Conduct, it is illegal to ...
  2. Under the The Red Room Code of Conduct, it is illegal to ...
  3. Under The Red Room's Code of Conduct, it is illegal to ...

#1 and #2 is what you're debating to use. #3 avoids this entirely, because the possessive attaches the object in question (the code of conduct) to the entire proper name (The Red Room). There is no ambiguity here, and no repeated words.