A Present, Present
noun
Remember 贈る, which means "to give a present"? A thing that you give as a present is a present.
おくりもの
The reading comes from 贈る and 物.
「これ、君への贈り物。干しふぐだよ。気に入ってもらえるといいけど。」「有難う。聞いただけで既にとっても気に入ったわ。」
"Here’s a present for you. It’s dried Fugu. I hope you like it." "Thank you. Just hearing that makes me happy."