His name was purely based around one joke- the "Achilles, heel!" line in the original movie. He quite nearly ended up nameless, but due to that one play on words, he received his name.
Also later in the first movie, during the final fight, Phoebus says "Achilles, sit" and the horse sits on an enemy's head. In the 2nd movie, during the Festival of Love, he found love in the end.
- Achilles was named after the Greek hero from Greek Mythology.
- A running gag is Phoebus telling Achilles to sit which results Achilles comically sitting on a person.