It's definitely not a standard name, but I call kind of reasoning error "active/passive bias": we're generally much more afraid of risks that manifest from action (mauled by a shark while swimming, getting in a car crash) than inaction (dying of obesity, getting hit by a car on the sidewalk).
In the case of COVID-19: you have to actively get the vaccine, meaning that people overweight its risks relative to the risks latent in not getting it.