Should my application name relate to app icon? For example if I want to name my application apple should the icon be an apple icon?
It depends. Ideally, what the application does would be something related to "Apple", so the name, function, and icon are all aligned.
However, if your "Apple" application is used for, say, painting, a paint icon might work better. Then it becomes your decision on whether to align the icon with the application's name or the application's function.