As Salaamu Alaykum
No, it's not true. Though, I've heard that the Sahaba used to do that (or rather, the Sahaba used to finish the Qur'an a week after they started).
You don't HAVE to, but it's a good thing to do so.
Remember, though, that the Prophet Muhammad
saw
said that if one finishes the Qur'an in 3 days, he/she didn't focus on it's meaning. So don't rush to read the Qur'an, but rather focus on it's meaning.
Personally, I believe it's better to finish the Qur'an in 5 years while knowing what it means than to finish the Qur'an in 40 days and not know what the heck you read or why you read it.