The lower cylindrical portion of the piston which improves piston cooling performance is called

valve recess

The crescent shaped cavity on the piston head top surface is called as valve recess.

crankshaft

The connecting rod connects the piston and the crankshaft.

to transmit motion of the piston to the crankshaft

the function of a connecting rod is to transmit motion of the piston to the crankshaft.

piston pin

The connecting rod is attached to the piston by the piston pin.