Vaccine Card name different from passport name

As the title suggests, I have not updated my passport yet – therefore it has my maiden name – but my vaccine card has my new married name already. Did not think this through when booking flights and hotel (St Lucia). Has anyone had a similar situation and encountered a problem?

Anyone know how to best resolve?

Edit: To add, I have a drivers license that has my new married name that matches the vaccine card. It’s just my passport that does not at this time.