Homonym have to be both a homograph and a homophone, or can it be just one or the other? As with most things in life, it depends on whom you ask.
Homonym must be both a homograph and a homophone. So say many dictionaries. However, other dictionaries allow that a homonym can be a homograph or a homophone.
With so many notable resources pointing to the contrary, are we losing this strict meaning? What then will we call a word that is spelled and pronounced the same as another but has a different meaning? If homonym retains all these meanings, how will readers know what is actually meant?
The careful writer would do well to follow the strict sense, ensuring his meaning is understood immediately.