How to set contact name during Drupal's user registration?
By default CiviCRM comes with a profile called 'Name and Address' which is set to be used for User Registration. First Name and Last Name fields in this profile are, again by default, set as required fields. So when a site visitor goes to user/register they need not only to provide a username/email address/password, but they also see the fields exposed in the Name and Address profile and must provide First/Last name. Maybe you've disabled or removed this profile? Or you can create a new profile that's used for user registration.