There are two distinct problems. If you want to own a trademark untraceable to you I am sure there are ways to do that, but they would take time and money. Probably some combination of LLC or trusts. Each state and most countries have some form of LLC and there has to exist some that suit your purpose.

But I am not sure how effective this would be in combating scams like you mention, because the due process might take too long. Probably a more immediate response like mobilizing your followers to protest would get a quicker answer from Twitter.