"Otomatone", is it made by combining "sound" and "hand"?
Wiktionary confirms that "oto" is "sound", but not that "mato" means "hand".
Sources: Google Search 1, 2, 3
What does Otamatone mean in Japanese?
Its body is shaped like an eighth note (quaver) where the sound emerges from its mouth on the notehead. This two-handed synthesizer instrument’s name Otamatone is a combination of two words – “oto” which means sound and “mato” which means “hand sound”.
While Wikipedia implies that the name's based on "otamajakushi":
The Otamatone is a synthesizer whose body is shaped like an eighth note (quaver) (it also somewhat resembles a tadpole, or a ladle, otamajakushi (お玉杓子 / おたまじゃくし) being Japanese for tadpole and ladle)
The translation of which is backed up by Wiktionary, of course, and Jisho.