The relevant text: "Whoever...utilizes any device or software that can be used to originate telecommunications or other types of communications that are transmitted, in whole or in part, by the Internet... without disclosing his identity and with intent to annoy, abuse, threaten, or harass any person...who receives the communications...shall be fined under title 18 or imprisoned not more than two years, or both."
There are three problems here. One is the definition of annoy. It's vague. It's variable. It's not something that can be easily gauged. What annoys me may not annoy you, so whose definition should I use? Should I ask first? "Excuse me, sir, but will it annoy you if I tell you that you are unmitigated horse's a55? It will? Okay, then I will not do so."
The second problem is the definition of "true identity". I mean, really - is my true identity my married name, my maiden name, my full legal name, my nick name.. what constitutes "true identity"?
And the third problem is - how the heck are you going to prove that I'm me on a web site? I can register with a hotmail account and tell you I'm anyone I want. Not that I've ever done that or anything.