Speedy

I started rewatching Young Justice, from the beginning, and I noticed something in the first episode.

"Today's the day."

Fans and audiences are witnessing the inclusion of sidekicks into the fold, working more closely the Justice League. While the young heroes make their way into the Hall of Justice, an audience asks, "Is that Batman?", while a female fan remarks, "Oh my goodness, I see Flash and Flash Jr." Another audience interjects, "He's name's Speedy, duh..." but is corrected, "No, Speedy's Green Arrow's sidekick." The last fan remarks, "Well, that makes no sense."

Sorry for the poor narration, I was my attempt at painting the scene I'm referring to.

Why is he named Speedy? And why's Flash's sidekick named Kid Flash?