I do wish you good luck on this because old bands are usually quite untraceable. For one thing, there is no national registry because each US state has its own rules as to what kind of bird requires them and how they are supposed to read. But, for another and in my own personal experience, breeders, for some particular reason unknown to me, don't seem to 'last' many years. Even huge birdmills seem to disappear over time... I remember years ago when a Florida breeder put out over 400 pairs for auction (and that was not even the total amount of birds she kept!) because of divorce (needed to split the 'assets'). Epidemics in the aviaries are common and, as they wipe out the birds, they also wipe out the breeders. And small breeders go out of business all the time - family situation changes, they need to move, breeding stock dies and is not replaced, etc. I know of a couple of small breeders (the only ones I know and not personally but from regular seasonal postings on CL - which I flag ) that quit because of Covid - and I also know of another couple of breeders that used to breed parrotlets that ended up with so many 'returns' that decided to stop doing it. And then there are the ones that started because they loved birds and realized they were doing them a huge disservice by breeding for the trade and went into rescue, instead. It doesn't seem to be a 'steady' industry - thankfully for the poor birds!
But, if you don't mind my asking, why do you want to know the name of the breeder? It's not as if it's going to tell you anything about the bird...