The FAQs on the Costcotravel site indicates that the designated principal driver should be a Costco member. In practice, I’ve never been asked for my Costco card at pickup, but I do have it with me, so I cannot really say what your experience might be. You do need a Costco membership to book the reservation, but the Costco rental car reservation form just asks for the name of the principal driver. Once you have the booking, you will have both a Costco confirmation number and an Alamo confirmation number on the email you receive from Costco. If you join the free Alamo Insiders program, you can then go to the Alamo site and associate the Alamo reservation number with your Insider account and manage everything from there. This includes adding the free second driver included with a Costco booking, online checkin, and skip the counter checkin. This last allows you to go directly to the garage to select your vehicle and then just hand over the Alamo skip the counter form with your drivers license and credit card at the exit gate from the garage. Very efficient.
Also, note that Costco actually suggests that you simply book a new reservation if you want to make changes, then cancel your original reservation. You do this by calling the 800 number on the Alamo web site. It’s an automated phone system so you can cancel an Alamo reservation very quickly using your phone without even talking to a customer service agent.