Unfortunately, at this time you cannot customize it. The options are to use the original registration page from the live webinar, or the minimal Share link that only asks for the name and email address.
Hi Jenee, the options Glenn is referring to are only available for webinars recorded using the online recording feature. There is also a setting under Registration Settings called "After the webinar ends, new registrants view a recording" that you will need to select as well.
Although GoToWebinar Recordings that are manually uploaded cannot customize Registrations at this time