I had a similar issue when the first pharmacy sent my shot information to the state health department with Middle Name/Last Name instead of First Name/Last Name. I went back to the pharmacy and they changed it and resubmitted it to the state. It took about a week before the state's records were correct but now it downloads correctly showing all three shots for me.
We tried doing that. The pharmacy said they could see both shot records, but they're on different computer systems. Same name and birthdate in both places, but no explanation why they're on two different records. We said, "Well, since they're both him, can you just join them together in one account?" Nope. They don't have the ability to do that. "Can you call someone who has the ability?" We can try. Days later, no change. It was agonizing. Surely we aren't the first people to have a mistake made on a name. But in this case, apparently it's too complex for the pharmacy staff to correct on their own.
Today we called the Nevada state people who track such things, and who are the ones showing only the second shot. Talked to them about it, explained what we thought we knew. They checked, and in just a few seconds, they said, "Yes, we can see both shots. Yes, the name and birthdate is right. The issue seems to be that the first shot has an address in Washington state." Huh? We used to live in Washington state, and somehow, the pharmacy used that address instead of our Nevada address when they set up his account down here in Nevada expressly to get a Covid shot. Not sure how they even got hold of that old address - all the ID has the Nevada address on it. But the Nevada state people just fixed it right then and there. And now, finally, both shots appear on his State record. We've printed out that record, just in case, to show it's another validation of the shot history.
Needless to say, if we ever need to deal with that pharmacy again, we'll make sure they use the right address! And now, we'll also find out if the Safe Travels folks in Hawaii do more than just read the uploaded vaxx card image.