There are algorithms to spot both similar text and similar images. I imagine that it would be possible for Twitter's sign-up process to say, "Hmm, this name is awfully similar to that name. And the avatar is the same as well. Maybe they're trying to imitate them?"
The problem is what to do next. Twitter don't want to pay an army of employees to vet every similar-sounding account. And if you asked the existing account holders to do it, they'd both make mistakes and abuse their power (for example, to block "This Company Sucks" accounts).