In a recent flight, I received the handoff, "27D change to Chicago
Center on xxx.xx" Next call, "Chicago Center, Arrow 27D, 3000"
Response: "Arrow 27D, this is not Chicago Center, this is Chicago
Approach". Me "Arrow 27D, correction noted"

Is this an issue of sufficient importance to waste the air time in a
very busy airspace? I'd just like to know...