I know that the person who is distributing something is called a distributor. what do we call the persons to whom the distributor is distributing.
The word that is generally used in the shipping industry to describe the person who receives a package is recipient. Consignee can also be used; however, consignee is most commonly used for recipients of commodity shipments and is not a very commonly used word. Receiver is another option, but this similarly is not as broadly applicable as recipient, and generally applies specifically to the person in the role of receiving packages for a business when used in this context, and can be confused with its other meanings for a part used in radios and telephony or as a member of a team for various sports.
Consider donee. From Merriam–Webster’s definition:
a recipient of a gift