Images from the Department of Defense show what Covid-19 vaccination record card and vaccination kits will look like. Vaccination cards will be used as the "simplest" way to keep track of Covid-19 shots, Everyone will be issued a written card that they can put in their wallet that will tell them what they had and when their next dose is due.
Vaccination cards will be issued to everyone getting COVID-19 vaccine. See story here. https://abc7chicago.com/health/vaccine-cards-will-show-who-received-covid-19-shot/8468637/