We've filled several assumed name certificates (Doing Business As) for online projects using the brand name before the TLD and opened business bank accounts for them. I have never included the TLD in my filings, but I have also never seen anything that prohibits it.
I have seen Federal Trademarks filed that include the TLD, so I would imagine that most counties local tax offices would allow such registrations for DBAs too.
Not an attorney, so just speaking from my limited filing experiences.