WSJ [paywall] – Doctors answer questions about preparing for the Covid-19 vaccine: “…Will you get a record of your vaccination? Adults will receive a vaccination card that includes the lot number and name of the administered vaccine along with a reminder to get their second dose. Those going for their second dose will need to bring this card with them. Your vaccination data is also recorded by the vaccine provider and stored electronically, Dr. Boom says. Later, you may need your vaccine document for work or travel purposes…” [This feature is powered by text-to-speech technology.]
See also this guide from Sarasota Memorial Hospital – COVID-19 Vaccines: What You Need to Know