Hi Liorah,
I’m afraid this sort of capability is not baked in to WooCommerce Tickets.
Collecting custom order data at time of checkout is probably the best way to do this, but at this time that is a customization you’d have to drive forward under your own steam.
Following feedback from lots of customers, though, we are actively looking at ways to help people with this sort of task and so perhaps you’d be interested in getting an early taste of what’s to come by participating in beta/usability testing? Please see the following post for more on this:
theeventscalendar.com/tickets-attendee-meta-functionality-seeking-usability-testers