Adam,
The Duff Gordons were travelling under the assumed name of Morgan to avoid publicity and so that they could have some privacy. Lucile was famous and hounded by the press (and loved every minute of it) but Cosmo would have nothing of it. He got to spend very little time with her owing to her busy career and did not want to share her with shipboard nouveau riches or tabloid reporters at dockside.
So she came up with the Morgan pseudonym as a sort of in-joke aimed at THE Mr. Morgan who was supposed to have been en route but decided against it - opting for a little frisky fun with his mistress. Lucile, being a close pal of Morgan's daughter, Anne Morgan, would have been well aware of this gossip.
Randy
PS) Its been discussed elsewhere here (though I can't remember the thread) about how she sometimes travelled under various aliases.