In the US at least we sometimes say 'squid' to translate 'seppia'. 'Cuttlefish' sounds rather British to me ...
Often Italian dishes call for 'nero di seppia', the black ink that these animals -- whatever we call them -- produce. In that case I've seen translations like 'squid ink', or if the squid is included, 'squid in their ink'.
Manhattan clam chowder has clear broth, plus tomato for red color and flavor. In the 1890s, this chowder was called "Coney Island clam chowder" and "Fulton Fish Market clam chowder." The name "Manhattan clam chowder" became attached in the early 1900s. Restaurants typically serve New England or Manhattan chowder, but not both. Rhode Island clam chowder has clear broth. Though less popular than the other two, clear, white chowders are still served, especially at long-established New England restaurants and hotels, such as those on Block Island.
I am not native but when I read "brodo con seppia" I imagined it would be a soup with the black ink the fish produces(as flaviano also mentioned). I have had of Pizza con seppia and that was pizza with squid and the black ink that it produces.