Well, I'm no KML expert, but I learned a few things by experimentation...
When I looked at the KML file in Google Earth and Google Maps, I was unable to draw the layer using any sort of classification (eg, based on a field value). It seems I can only control the drawing of a feature on a per-feature basis. So I assume the author of this KML went through and picked the polygon fill symbol for each feature.
When I opened the KML in Notepad, I saw where ArcGIS Online was getting the text for the legend values. The polygon symbols are defined in the KML and each feature references a symbol. Each symbol has an ID, like "PolyStyle00". I renamed all instances of PolyStyle00 to "Vacant" and that showed up in the legend of ArcGIS Online! So that's a way to make it work.
After all that, it would be useful if a map author in ArcGIS Online could edit the legend text. I can write up an enhancement so it's in our system, but realistically, I don't see this being addressed in the near term, based on our current schedule.
Thanks,
Mike