I remember someone calling him "The Hawk" near the start, saying he was in "his nest", but I don't remember "Hawkeye" specifically. I'll have to keep an ear out for it once I watch it again (cause I know that's inevitable).
OMG! You actually got Hawkeye right!!!!! Very few ppl can actually get his face to look like the actor..and without drawing him in that AWFUL purple suit...XP I applaud you! (Applause) and if yu clicked on my favs, yu'd see about a billion of your comics XD