It is said that there are just bits of fried tenpura batter and no 'tane' (ingredients) and, in other words, 'tanuki' is a collapsed form of 'tanenuki' (without ingredients).
天ぷらのかわりにのせる＝「タネ」がない、つまり「タネ抜き」がなまって「たぬき」。