We do have an opportunity to choose the vaccine in a roundabout way by asking the person giving you the shot to produce the vial so you can grab a photo, if it's not what you want you can have a conversation at that point. Not sure if there are quirky laws elsewhere but I've always been made to sign off on a form that says I got the "VAS" that also has a line that lists the manufacturer and lot number and grab a photo right then and there, did the same for my children when they were young. It's best to ask caregivers to bring the actual vial when escorted back so they can carry it along with the needle otherwise they can end up searching for it. Only once did they bring me the wrong type of Flu vaccine in over 20 years, not that it would have mattered much but it's my body.
I'm all for vaccines but this is an informed consent issue and I'm all for that too. The more transparent things are the more likely people will be to comply
Read fact 9, very last point:
https://www.immunize.org/catg.d/p2027.pdf
That's not exactly what I was discussing though. If a person says "I'm going to wait until I can get a vaccine that is the best or has a higher efficacy rate than the one initially given" my point was they may not have a choice. We are under this with the entire globe trying to get the vaccine for all their citizens. Choice is not a luxury we will likely have or at least I wouldn't bet on being able to decline a COVID-19 vaccine because there will assuredly be another option available and quickly. Think about how many new vaccines came out in the past, most didn't have a choice what was there initially. It took years to get different types as development could occur and vice versa where over time options were lowered. This is also why I understand the hesitancy regarding being one of the initial people.
What you did with your kids when they were young I'm not sure would even be possible right now. I think it's likely much greater you'll get the vaccine available or you'll choose not to but you may be waiting an undetermined amount of time before a different vaccine has been secured by your country and then filtered down to be used in your doctor's office.
Just to give an example the HPV vaccine. Right now there are 3 that are cleared for usage in the U.S. by the FDA according to the CDC "(9-valent HPV vaccine (Gardasil® 9, 9vHPV), quadrivalent HPV vaccine (Gardasil®, 4vHPV), and bivalent HPV vaccine (Cervarix®, 2vHPV)" but only ONE is currently being used in the U.S. "Gardasil-9 (Merck), a nine-valent HPV vaccine (9vHPV) that protects against HPV types 6, 11, 16, 18, 31, 33, 45, 52, and 58, is the only HPV vaccine currently distributed in the U.S." In the U.K they use Cervarix instead of Gardasil.
Now the reason only one is being used in the U.S. my assumption is the protection against more types has gotten more encompassing but that still took years to get to that point. The first Gardasil was in summer of 2006. The one currently used was approved in 2014 when the other ones were discontinued in usage in the U.S.
This is all purely guessing at this point but I just wouldn't set myself up for thinking I would have a choice much less be able to take a picture, look up all that information in the doctor's office and decline if I wanted to in favor of getting a different COVID-19 vaccine.