The square and orange background are completely unnecessary. They don't really add anything to the design or say anything about the identity of your friend's business. It's all in the face. Looking at the face alone I wouldn't guess it was a hat company right off the bat. Looks more like an avatar or icon for chat. You may get away with cutting the face too, as cute as it is. Or at least somehow arrange it so the hat stands out more. Hats themselves can definitely be iconic. Considering adding type too, that would help sell the idea of it being a hat business. Maybe some text wearing an eared hat.
"Astronomy offers an aesthetic indulgence not duplicated in any other field. This is not an academic or hypothetical attraction and should require no apologies, for the beauty to be found in the skies has been universally appreciated for unrecorded centuries."