Depends what you term as 'off brand'
Shotguns: Name Brands were Browning, Ithaca, Remington, and Winchester.
Mossberg was the 'off-brand cheap competitor oh you can't afford a Remington huh'?
NOW, Mossberg is considered name brand. Maverick is considered the economy option, and the 'off-brands' are now EEA, Escort, Geforce, Retav, Tristar, etc.
Rifles: Weatherby was on top, Winchester and Remington held a huge amount of ground, and a few other brands like Browning (Steyr, and Sako if you were European) were considered good guns.
Ruger kind of sat out there on it's own between the two camps.
Savage, Stevens, Mossberg - they were all aimed at the guys who couldn't quite afford a Winchester or Remington. Howa and Tikka joined those lower ranks.
Now, Remington is dead Winchester isn't much different, Savage, Tikka, Howa are all considered recognizable brand names, and the 'off brand' are really economy rifles carrying a name brand - the Savage Axis, Weatherby Synthetic, the Ruger American. In actuality those are off-brand rifles bought and then absorbed by the big names. You don't really have any off-brand rifles.
For other goods? I don't feel compelled to buy 3M brand post-it notes, off brand are fine. Same with toilet paper or tooth brushes. Interestingly, I've not seen many 'store brands' invade the toothpaste aisle. If I'm going to buy a vacuum, the 'name brands' such as Hoover and Dirt Devil, I don't consider that brand name to impart any sort of quality. I expect all $50 upright vacuums found at walmart to be the same low level product regardless of what brand name it has - be that hoover, black&decker, bissell, dirt devil, shark, whatever. I expect all $250 vaccuums to preform about the same and be much better, even though it's the same set of brands as listed before. 'off-brands'
For food - store brand milk just as good as Land o Lakes or Kemps. Store Brand chicken noodle soup just as good as Campbells. Most 'name brand' food means you are buying boxed and processed stuff, which means you are already buying low quality product so it doesn't really matter which way you go. As far as fresh fruits, veggies, meats, and spices - there aren't really name brands liked to them in a meaningful way. I'm looking at what appears to be inside that container of grape tomatoes not what brand is on the plastic.
Some food additives such as olive oil, there is where you'll find a difference in quality, but I can't say any of the good olive oils have any sort of name brand recognition except reading reviews or getting recommendations from chefs, friends, food blogs, etc will make me look for certain brands. But it's not really the same as brand recognition.
For tools, I tend to buy the mid-range stuff as I don't work em that hard anyways. Yea, I'm not going to buy the $10 shovel from Fleet Farm, I expect that to break. But the $20 seems to hold up just fine.