Certainly! This could be handled in different ways. If doing individual registrations, the default "firstname" and "lastname" fields are the registrant. That does NOT have to be the billing person. You could create other fields for parent info, or whatever else.
Also, in a detailed group registration, every registration has data for each member of the group, then the billing/contact info. That is ideal for parents registering kids, etc. If that is a common thing for you, maybe consider setting the event to only accept group registrations, but set the minimum group size to 1.
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