The site that says Atreyu means "boy warrior" is obviously taking a description of the character in Michael
Ende's Neverending Story
and using that as the "meaning". But that's not really the same thing as an etymology.
It's possible that Ende simply made up the name. However, there is a Sanskrit name Atreya, meaning "belonging to Atri", and it's possible Ende altered that to come up with Atreyu. But one would have to have confirmation from Ende himself to be sure of that. Unfortunately, he is now deceased and I don't know if he ever wrote down anything about how he chose character names.