1. A good question. Have you tried figuring out the answer yourself?
2. Have you been in the Beast's Outer Lair?
3. Have you ever tried saying your name as the Beast demands?
4. There are at least a dozen ways to say your name: SAY MY NAME or SAY "ARTHUR DENT" or SAY "MY NAME IS ARTHUR DENT" or SAY "I AM ARTHUR DENT" or TELL THE BEAST MY NAME or TELL MY NAME TO THE BEAST. You could also say BEAST, MY NAME IS ARTHUR DENT or BEAST, I'M ARTHUR DENT. There are some others but you've probably got the general idea by now.
5. You have to give your correct name to the Beast, or (in a rare moment of Bugblatter Beast perceptivity) it will be able to tell that you're lying. In addition, you can't tell the Beast your name if the Beast thinks it can't see you.
6. The Beast's response when you told it your name should provide an additional hint toward why the Beast wants to know your name and how to solve this entire Traal puzzle.