Dannon \d(an)-non\ as a girl's name is a variant of Danna (Old English). See for meaning of Dannon.
The baby name Dannon sounds like Deneen and Toinon. Other similar baby names are Nanon, Danny, Danni, Danney, Dannia, Dannee, Dannah, Darion, Daron, Danne, Manon, Reannon, Riannon and Shannon.