Homonym means each of two or more words having the same spelling and/or pronunciation/production but different meanings and origins. Like spoken languages, signed languages have homonyms.
An example of homophone (or "homosign") in ASL is the same sign for the number 'nine' and the alphabetical letter 'F'. Or, the ASL homonym 'BROWN' looks like 'BEER' (two movements -- though, the movement of BROWN can be either one or two repetitions, not interchangeably). Both ASL signs BROWN and BEER have different meanings and origins.
Many Deaf people native to ASL have been signing them ever since and these homonyms have not really dawned on them. From time to time, my ASL newbies with their fresh eye (or a beginner's Zen mind) came to me and expressed their confusion for a homonym pair of ASL words. Sometimes they surprised me that I hadn't thought of them before. I'd usually tell them "context." And practice ASL conversations if they are not used to contexts.
Just for fun. As of this writing in a goofy mood, I grabbed my camera and turned to my nine-year-old bilingual girl who was never confused between the number nine and the letter F. I raised a single, standalone syllable F/9 out of blue sky. Out of context.
Thoughts raced in her head, seeking a context for this meaning. One of her some thougths was "Is this some kind of a trick?" "What is going on?" "Why did Mom do that?" "Strange." "Is that a F or 9?" She has never had this difficulty before unless it was out of context. If she were an adult, she probably thought of a gesture itself meaning something else in other countries. Then again, F/9 in ASL is a word, not gesture (because processing is different in the brain).
Occasionally, an ASL student would ask "why are this sign and that sign the same production?" Among many other phonocentric thoughts, this implies homonym is acceptable in English but not expected in ASL. We'd point out that English has plenty of homophones and homographs that don't really raise a concern. ASL is no exception.
More common homophones or homonyms in ASL that I realized from my ASL students (as I naturally recognized only meanings without noticing their same production/pronounciation): THANK-YOU and GOOD, YELLOW and ARABIC, WISH and HUNGRY, MONTHLY and RENT, and so on.