Hm...Maybe Jack Andrew Dawson Jr. ...Doesn't sound very good, but still that if going by the canon storyline in which Jack didn't get out of the ocean.

In any case one of his names should be Andrew, in memory of Mr. Andews who - (in addition to Jack of course) - was the only likeable man in the bunch of men in Rose's life on the ship...He was the only one with sense and he was always so nice to Rose...I can bear the assholeness of the others and the stupidity of the captain simply because Mr. Andrews was so nice. And I feel sorry that he blamed himself for what wasn't his fault in any shape or form. I really like the character so I'd like Rose to name her son after him.

I could see Rose wanting to name their son after Jack

I think this would make sense because they would probably be naming him after two men. Thomas Andrews and Tommy Ryan. I don't know, just a thought.

Rose would have wanted to name their son after Jack and I think that is what they would have done.