"But I had the idea first."Ideas aren't IP — the execution is. First to think of it doesn't win; first to make it real (and, for names, first to use or register) does.
"We made it, so we own it."Not always. If a client paid, they often own it. If a freelancer made it, they might — unless your contract says otherwise. Existing and owning are two different questions.
"It's a brilliant strategy."Strategy usually isn't ownable. If it's your edge, your protection is keeping it secret — not claiming it.
"It's on our website, so it's ours."Publishing doesn't create trademark or patent rights — and it can end a trade secret the moment it goes public.