Why is the book titled The Old Man and the Sea, not The Old Man and the Fish?
I guess some reasons could be that 1. The Sea title better fits the focus of the book (Santiago's relationship with the sea/his struggles with it) or 2. The Sea title better describes the theme(s)/lessons of the book---like perseverance in difficulty (the sea really shows this, and all the creatures in it, not just the marlin) or 3. The Sea title better shows the true antagonist of the book (the sea, not just the marlin) or something like that. What might some other reasons be?
I think you've developed three very plausible explanations for the title of the story. The aspect that you're overlooking in all of your reasons is that love of the sea that also figured strongly in Santiago's life and attitude toward his surroundings. Certainly it was a struggle to locate the fish and hard work to catch and land them. There were difficulties of distance and heat and threats from jellyfish and sharks, but there also were beautiful colors and graceful movements, and there was the pride of being independent and able to succeed in ones work. The story tells of the love-hate relationship Santiago had with the sea and all the creatures who lived in it, the changes that occurred on it, and the impacts those interactions had on his life.