Well iconic, something where it's probably more about the ship and the crew vs it just being a "vessel" for the story to take place.
I mean Alien could take place on a shuttle ;-). Event Horizon a house, the setting is just the ship, the ship isn't a character in the story.
Like you say Mass Effect, you think of Shepard, the crew and the Normandy, you think of Star Trek you think of Kirk, crew and Enterprise. You say Alien, you think of Ripley getting out the cryo in that skimpy outfit, the cat, the droid, the alien

but not really the ship.
That would be an iconic ship, not just one in a story
, a lot of people wouldn't even know the name of the ship in Alien, nor even in 2001, as that isn't really the focus. Nerd though...