I thought it was an awesome choice. "An" is a Vietnamese given game, or first name if you're from the west like me. I was born and raised in Canada so my native language is English. My family is Vietnamese and they made me go to Vietnamese Saturday school to learn how to read and write their language. I had and still have difficulty distinguishing the sounds of some letters like "a", "ă", and "â". This example is so helpful because it helps us recognize how the letters "a" and "ă" are pronounced without any tonal accents, while teaching us a little bit of Vietnamese culture.
Yes, "An" is a Vietnamese name while "ăn" means "eat". Note that "a" and "ă" are two different letters. That's why they sound different. I also want to point out that both words in the sentence have a leveled tone ("ngang"). So you really are learning how each letter sounds =)