Answer:
My first half is normally made of stone, my second is crazy, and I taste sweet when complete.
I am never quite what I appear to be. Straight-forward I seem, but it's only skin deep. For mystery most often lies beneath my simple speech. Sharpen your wits, open your eyes, look beyond my exteriors, read me backwards, forwards, upside down. Think and answer the question...
My first is nothing but a nameอพ my second is more smallอพ my whole is of so little fame it has no name at all.
Though desert men once called me God, today men call me mad. For I wag my tail when I am angry. And growl when I am glad.
They made me a mouth, but didn't give me breath. Water gives me life, but the sun brings me death.
What never gets any wetter no matter how hard it rains?