You can use the contact us on the website and provide them the information. They will need to cancel the reservation and rebook it, giving a new reservation number.

When I became gold it was about as simple as that.

From their FAQ's (which not exactly the same thing, but it's about adding a gold number to a reservation)

https://hertzhelp.custhelp.com/app/a...20reservations

Forgot to add my Gold Plus Rewards membership to my reservation

I forgot to add my Gold Plus Rewards membership number to my reservation; is it too late to add my number?

In order to add your Gold Plus Rewards membership number to your booking, the reservation must be canceled and rebooked. To do so, please contact Hertz Reservations. Click below to Contact Us.