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We actually do have a name for the back of the hand it is called the dorsal or the dorsum;which is latin for the back of an organisms body part. It would be the hand in this situation

DORSAL

•   The adjective DORSAL has 2 senses:

1. belonging to or on or near the back or upper surface of an animal or organ or part
2. facing away from the axis of an organ or organism

That applies to all organisms and of course us humans. The palm is more frequently used though. We experience more things with our palm also. We eat and we do productive things with our palm. There's nothing to do with the back of our hand and a backhand slap doesn't count. If you do find something else that we can do with the back of your hand please inform me.
http://www.meddean.luc.edu/lumen/meded/medicine/pulmonar/pd/pstep74.htm This website basically shows a demonstration of both sides of our hands.