I've spent years complaining about how I think it's been unreasonably difficult to purchase a Camp Half-blood t-shirt for the kids in my life who are fans of the PJO book series. Since the TV show, there have been official shirts, sure, but I think the first time I checked, they weren't actually being sold in my country? (I do not need any advice on how to acquire shirts. I have acquired the shirts, thank you.)
This rant has also extended into how I think it's kind of silly that all of these different publishers wouldn't also go the extra distance to make t-shirt and other merchandise designs for EACH individual cabin. I think fans would have gotten a real kick out of that even if individualized cabin t-shirts aren't the canonical book designs. I think it's fun. It just seems to me like this should have been an obvious merch avenue from the beginning, you know?
And recently, while talking with one of those PJO fans I bought shirts for, I extended the individualized cabin shirts rant into how I think this is also a missed opportunity beyond merchandising... I think it could have been a fun and interesting visual storytelling tool in the TV show or in the movie adaptations.
Like, logistically in-universe, going by everything else at the camp, it would be so, SO easy for a Hephaestus or Apollo or whoever kid to set up a screen-printing station or whatever. Or for the camp to acquire fabric markers in bulk or something. Decorating t-shirts is a not uncommon, classic camp activity! (Tie-dye. Someone at this camp is doing tie-dye.) I think we can also say it's reasonable that these kids might want to show off their personal style AND cabin pride however they can... and different cabins having different shirt designs is a way to do that!
For example, let's say that Annabeth's shirt says "Athena Cabin" underneath "Camp Half-blood". Maybe it has the cabin number on the back, and maybe her name "CHASE" is printed above that. To get fun with it, maybe there's an owl above the front lettering and it's all framed by olive tree branches or something. Maybe the sleeves also have little olives and leaves! Elegant style. Exact design doesn't matter.
The point narratively: campers look at Annabeth and instantly know who she is and where she belongs. Good for a visual medium. GREAT contrast against Percy when he first arrives... because Percy's shirt will be blank. No cabin name. No number. No stylistic flourishes claiming him as part of a recognized group. MAYBE someone scribbled "JOHNSON" on the back of his too-big shirt in permanent marker, because that's what they were told the name was and they don't want the kid's clothes to get mixed up with all the other unclaimed campers' clothes in the laundry.
I like the orangeness of the shirts, so I think I'd keep them all orange, but if I wanted to be EXTRA obvious about this... I'd make all the cabins have different colour shirts. Athena in gray, Apollo in yellow, Ares in red, so on and so forth. Exact colours do not matter to me EXCEPT 1) Poseidon Cabin's shirt (probably a deep sea blue) stands out sooo clearly from the crowd. As soon as Percy is claimed, he visually stands out as a lonely outsider among everyone else.
2) Hermes Cabin's colour needs to be that basic orange and all the unclaimed campers also need to be given orange shirts (though only Hermes kids actually have the cabin name and number officially on there). You can then have Luke express some wry bitterness that Hermes kids don't get their "own thing" because their cabin has to take in all the "unwanted" kids too.
Again, personally, I like the orange, but I do think changing the colours per cabin would be a valid artistic choice (I don't think they're getting around to the sequel series, so I don't think it's a concern, but you could make a point that no one wears purple). In-universe, it would be easy to tell different cabins apart during capture-the-flag games this way. From a storytelling perspective, it would easily visual mark people like Clarisse and her siblings (Percy's antagonists initially) for the audience. And I do personally think being able to easily tell characters apart is more important in a show than sticking exactly to the book.
The other advantage to this is that you can do individualized character storytelling through costume as well. Maybe different campers would choose to decorate their shirts in different ways! Maybe some of them have added embroidery or patches. Maybe there's official camp decoration (cabin name, number, and camper name), then people add on to that with bleach or fabric markers. Some people are super creative and some people keep it plain.
Maybe campers who know their parent but aren't part of the official 12 Olympians decorate their shirts anyway with their own designs. Maybe campers who hate their parent have "vandalized" their shirts somehow to reflect that. Maybe older campers will pass on their shirts to younger half-siblings. Maybe campers will have both "fancy" new shirts to wear to special events, and more raggedy and colorful "casual" shirts just to wear around.
This would also give us the opportunity to see Percy's shirts evolve in various ways over the years. Maybe his first Poseidon Cabin shirt is kept pretty plain. Maybe the next year's shirts are decorated for or by Tyson somehow, and so on. Maybe by the last year (of the story), we see that Percy actually still has his orange unclaimed camper shirts sitting in his drawers in the Poseidon Cabin, way too small for him by the time he's 16, because throwing them out felt awkward and wrong.