No one assigns NAICS code.
Businesses choose their own codes and apply them to their corporate profile. It is a Self-Assigned System. Your business will pick the code for the industry they primarily fall into and use that code whenever they are asked for it. If the business performs services or provides products for more than one industry, multiple NAICS codes can be used. There is full manual you can download here
, or you can utilize the NAICS website
and search based on number or keyword.