It does not need to be specifically for puppies. Personally, I prefer the all life stages foods anyway.
No mammal, humans and dogs included, feed their young
different food from that adults get (post weaning, of course). Infants simply get proportionately
more food. That doesn't mean that all puppy formulas are bad. But having puppy on the label doesn't make a food good or even suitable for feeding either.
IMO you might as well just ignore the label. Read what's actually in the food instead

A food using high quality, meat based ingredients is far better than one high in grains - and it's a better thing to feed a pup than a grain based food that's marketed as "formulated" for pups (and there are many).
A couple of things to watch with dry food for pups though: you shouldn't choose a food that has a protein level much outside the 22-26% range (so none of the 6-star foods is appropriate - and that's stated in the food reviews on the review site), and calcium should preferably be in the 0.8-1.3% range (though not many foods even tell you that).
So the 6-star foods are really only for adult dogs. But there are still plenty in the 4 and 5 star range to choose from. Anything rated that highly is still very good.