He's more than willing to stand in silence while the kid pets his dog, it's for a good cause, honestly. This kid is clearly suffering from a dog deficiency.

When she speaks again he misses the first couple of words entirely, but they probably weren't too important because he gets the rest of it just fine to answer her question. "That's a bit of a story." Clint says slowly as he tries to decide how much of the story to actually share with uh, you know, kid.

"When I first met him his name was Arrow, but he was really hurt and probably shouldn't have survived. So when he did I decided to call him Lucky because he's a pretty lucky dog. Aren't you, boy?" The wagging tail seems like answer enough to Clint.