I went to an internationally recognized “name-brand” residency program. What I will say is that the reason you would want to go to one of these places is the training, not the name recognition. The name itself can be helpful but it really depends on how you’re intending to practice.
In academia, people do recognize the names of the better residency programs and it probably helps a bit with hiring. That being said, a fairly large number of programs would get you to the same place in this respect. Academic positions often don’t pay as well, and they’re kind of self-selecting more than anything. I’ve known people from pretty middle-of-the-road residencies who have gotten jobs at MGH and people from my program who have taken jobs at more middle-of-the-road places. Part of the issue is that places with very big names (I think MGH and Hopkins might be some of the biggest offenders here but I think that a similar thing probably goes on at many of the places you listed) pay their attendings terribly compared to basically every other institution. So, if you’re going to work at one of these places, the name better be worth a lot to you (as in, almost $100k per year)
The two places I can think of where the name recognition of your residency can actually matter are forensics and certain forms of cash-pay private practice in more saturated markets. But even here, it’s not like anybody is going to quibble about one program vs another past a certain point. In these situations, you’re taking about lawyers, judges, and the lay public. They’re not doctors, and they’re certainly not psychiatrists. They have no idea what goes into making a residency program good. Most of these people don’t even know what MGH is, or how it’s different from BWH or BIDMC. All they will hear is “Harvard,” “Columbia,” “Hopkins,” “UCLA,””Duke,” “NYU,” or whatever. Distinctions don’t really matter at that point and all people are going to see is that you trained at what they perceive to be a top academic institution. That being said, if you’re going through voir dire to testify in a legal case, it will definitely be perceived differently if you trained at an academic place with a recognizable name versus if you trained at a community place that nobody has heard of.
As I said, if you’re trying to do a cash pay private practice in a saturated area, what I just said probably also applies. Having said that, most places in the U.S. are not saturated with psychiatrists. If you’re the only psychiatrist for miles, or there are a few psychiatrists but most of them are full and you’re the only one taking patients, you’ll probably wind up getting cash pay patients no matter where you trained. If you’re planning to take insurance, where you trained basically does not matter at all because you’ll fill either way.