There are no requirements, and they wouldn’t be enforceable even if somebody tried. The admin of instance1 has no way of knowing that you already have an account on instance2. Your identifiable details (IP address, e-mail address) are private to the instance that you sign up with and it would be a violation of privacy (and inherently scummy) for those to be shared between instances - they’re not.
You can be anonymous on the fediverse, just like the Internet in general used to be before Facebook.
That’s fine too, the short of it is it’s entirely up to you.