Is the chemical numbing agent in cocaine the same as chemical numbing agent in lidocaine and novacaine?

No.

They are three different things.

Cocaine is a neurotransmitter reuptake inhibitor.

Lidocaine and Novocain (more properly, procaine) are both sodium channel blockers, with the former being in the amino amide group and the latter being in the amino ester group.

The suffix "-caine" is simply a common reference to alkaloid anesthetics.  Like Amylocaine, benzocaine, tetracaine and several others.  Chemically, the alkaloids are related to each other, but they're not identical.