In cases where the Primary registrant isn’t the attendee, you can add more fields to the registration form to capture information about the person registering on behalf of the attendee. This way the kid’s name will show up in the registration list instead of the parent’s name.
Put another way: Instead of using the system questions like First name, Last name, and Email for the parent, use those for attendees. Then you build a new question group for the parent and fill that group with specific questions for the parent. You’ll assign the question group for parent information to the Questions for Primary Registrant within the event.
Once the questions and questions groups are all fixed up, you can set the Primary Registrants email template’s To: field to use something like: [PRIMARY_REGISTRANT_ANSWER_* Parent email]