"Soramimizuku" is a combination of soramimi (空耳, "mishearing") and mimizuku (木菟, "horned owl").
"To-What-To-Who" is a corruption of the sentences "To what?" and "To who?" which usually emulates being nosey. It can also be a joke on an owl's call like "Who" or "Twit Twoo (pronounced Tawit Tawoo)".
To-What-To-Who's Soultimate Move name is a reference to Soramimi Hour (空耳アワー), a late-night variety show that runs on TV Asahi.