What was the name given to a gigantic, luxury steam ship that tragically sank in the Atlanic?
The Titans are called the Elder Gods because they preceded the Olympians,were of enormous size and of incredible strength.
The name given was the Titanic. Your question though seems to allude to a wider theme, and that is the relationship between Greek Mythology and the sinking of the Titanic. A key concept that needs to be examined is that of "hubris".
"Hubris" was a key way to invoke the anger of various Gods, and there are numerous examples of foolish mortals who boasted too much and were punished as a result. The story of Archne is a case in point. This simple peasant girl claimed that her weaving was superior to Minerva's weaving. Minerva challenged Arachne to a contest which Arachne accepted and Arachne produced a work equal (if not slightly better) than the goddesses' piece of weaving. She split Arachne's weaving and beat her, and Arachne killed herself. As a sign of remorse, Minerva changed her into a spider and her skill of weaving was left to her.
Therefore, to the Greeks, such a quote "Not even God himself could sink this ship" was just asking for a tragedy to occur by placing man's arrogance and belief in their own skill before the strength and might of the Gods. Even calling the ship "Titanic" alludes to the Titans or the Elder Gods in Greek Mythology, who were supreme in the universe and were of enormous size and incredible strength. Atlas is one of the most famous of these.
Thus we can see that the Titanic was in a very real fashion thought to be a monument to the skill and accomplishments of mankind in Victorian times, and the oft repeated remark that the Titanic was "unsinkable" represents a sureness in the power of mankind's progress, based on scientific advances and ever-more-wonderful discoveries. With such a confidence, you can kind of understand why it was not equipped with enough lifeboats.
The Titanic was the luxury ship that sank in the Atlantic.