Event Registration Form: 
  1. Edit the Event Registration form part
  2. Click the Arrow beside Options
User-added image
  1. Mark the checkbox for Allow individual to register on behalf of organization in the Organization Options section
User-added image
  1. Mark any other Organization field options as needed
  2. Click Save at the bottom of the event form part

Event Registration Form Classic: 
The classic event registration form does not allow this option. The event registration form part will have to be used instead.