what is the name of part highlighted below?

I believe that is called a "Shift Lock Cover".

Correction: It's called a "Shift Lock Release Tab Cover". Some manufacturers are nice enough to even label them as shown in the picture below. It should be an inexpensive part that you should be to get dirt cheap from an auto salvage yard...or eBay, an online auto parts store..all else fails, from the local Honda Dealer (last resort).

thanks Racer_x. What is the use of this? How much should it cost?

you pop plug out and push relase linkage, So you can shift out of park when battery is dead.