Events tickets booking with Woocommerce is different than the default payment bookings

With Woocommerce we use the default checkout form to finish the tickets booking instead of a custom booking form. To edit the Woocommerce checkout form we recommend using this free plugin You can add any new field in the Woocommerce checkout form by using this plugin.

However to furnish registrant name on the ticket you need to enable registrant fields option from the WP Dashboard => Eventer => Settings. Enabling these options will have ‘Name‘ and ‘Email‘ fields by default for each registrant during the ticket selection. To add more fields for individual registrants see registrants form

Here is how individual registrants fields will look when you enable the individual fields:

Woocommerce bookings has 3 different views which you can check out here