His name "My Arm" derived from when he was just a baby. Trolls are named after the first thing they tried to (or successfully) eat. Since he first tried to eat his dad's arm, his dad decided to name him My Arm.
My Arm loves Goutweed, as do most trolls. Therefore, when he found out that it was possible to grow Goutweed, he wanted desperately to learn how. He even gets impatient and starts attacking stuff in a cutscene.
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