The title gets at an interesting question we’ve been pondering while reading this lovely little book: Why is the protagonist always referred to as "the old man?" Wouldn’t it piss you off if you were always called "the eighteen-year-old guy" or "the twenty-two-year-old woman?" Exactly. The old man is, for better or worse, defined by his age. He’s old, and the narrator details everything that he does (we’re being vague so you’ll actually read your book) without ever letting us forget his age.
Then there’s also the sea part. Note that it’s "The Old Man and the Sea," not "The Old Man and the Boy" or just "The Old Man." This lets us know that the old man is in isolation from people, but he's not really alone. There’s even this one line – "no man was ever alone on the sea."