A quick scan of about 20 on-line 'dictionaries' reveals some variance in the definition. Oxford (US english vers.) allows applying "homonym" to words that are -- and are NOT (their example: "meet/meat right/write/rite") -- spelled the same, so long as they are homophones.

http://oxforddictionaries.com/definition/homonym?region=us

English being what it is, JavaFan's advice (++) to check with a linguistics forum seems well taken.