Name for the central region of the human hand/foot?

Solution 1:

Sure, these are the 'metacarpus' or 'body of the hand' and the 'metatarsus' or 'body of the foot'. The anatomical/zoological terms ('metacarpus' and 'metatarsus') are also used, more specifically, to refer to the bones in those parts of the hand and foot, but generally, as determined by context, those are the terms.

metacarpus, n.
....
...the part of the human hand that is located between the wrist (carpus) and the fingers....

metatarsus, n.
....
...the group of bones...lying between the tarsus (ankle) and the phalanges (toes); the part of the foot...containing these bones.

OED, text emphasis added.