Spoilers up to and including the Sabaody Archipelago arc in the anime.
They call him Pirate Hunter Zoro. He's the sort of man that managed to gain relatively great fame despite living only in the weakest of all oceans, the East Blue. He has no mercy, they all say, he is harsh and evil and deadly. He's a demon.
Roronoa Zoro never cared about that. He did what brought him closer to his goal and not only did bounty hunting earn him money which kept him fed, most strong swordsmen were pirates. It was only logical.
And though he's not really all of those things they call him, he sort of is nonetheless. Zoro is deadly, and strong. He isn't actually a bad guy, but he's so vicious that it's hard for most people to see that. He fights who he wants and lets nothing stop him, and if along the way he impresses a few people with how cool or noble or brave he is, he leaves them behind when he goes to the next island.
He sleeps alone under the dark sky at night, and Zoro is never lonely because he has his three katana by his side. The spirit of Kuina drives him on and his sense of direction is terrible because he only looks ahead to his dream.
Zoro is quiet. He rarely speaks, and it is with a purpose when he does. He prefers actions over words, and actions involving swordfights most of all. He likes his rum, but he doesn't really get drunk, and he drinks with a solemn sobriety that silently warns others away. He's always alert but that doesn't mean he cares. Most of all, he travels on.
Some people would say his life is desolate and empty. They are the kind of people Zoro passes on the street every day without a backwards glance.
He doesn't care about anything but his goal. All that is in him is a quiet conviction: he will achieve it someday.
They call him Pirate Hunter Zoro. At first he was used to it if not approving, but as time went by he couldn't help but wonder why they still called him that. He is an established pirate himself now – first mate of the Mugiwara Kaizoku, with a bounty of 120 million beli. It's higher than most captains, let alone subordinates in crews, and Zoro stood right there with the rest of Luffy's nakama as they declared war on the World Government.
He never hunted pirates in the first place and if he had, he doesn't anymore. They still call him Pirate Hunter Zoro, though. The demon of the Mugiwara Kaizoku, one of the Eleven Supernovas; other titles come along the way, but none stick as that first has. Zoro isn't sure he approves.
He never liked the name, for the simple reason that he wasn't a pirate hunter. His feelings about it now are less certain and far more complicated.
Everything about Zoro is more complicated now; it has been growing steadily so ever since meeting Monkey D. Luffy, which is interesting since Luffy is such a simple person himself.
Zoro is the same man he always was but he's immeasurably different as well, and it's all due to Luffy. His Captain is the sort of man that does that to a person, changes them forever without even noticing, and it's not like the rest of the crew haven't been through a similar metamorphosis. But that also doesn't mean that Zoro is any less affected by his changes.
They happen so that he doesn't notice. Zoro has never had a sudden, identifiable moment like the rest of the crew. Luffy proved himself to the rest. He saved Usopp's village and Sanji's restaurant. He saved both Nami's village and her dreams by taking down Arlong, destroying that map room of hers, and declaring that she was his nakama. He recruited Chopper much the same way; Luffy protected the reindeer's flag and shouted to the heavens that he was Chopper's friend. Everyone knows what Luffy did for Robin: he gave her faith, made her belong and admit that she wanted to live. Franky was a witness to that even before he joined the crew, and if Luffy's method to get him to join – stealing his pants – was a little less dramatic and noble, he still made Franky cry and dust off his dreams. Brooke would have been glad enough to just be accepted by a living human being again, something Luffy did without hesitation – but the boy also rekindled the skeleton's hope by telling him of how Laboon still waited.
Everyone else can pinpoint a moment, where their earth shook and settled differently from before, where their hopes and dreams grew and seemed truly attainable. Zoro can't.
He can't because in many ways, there wasn't one. Zoro is the one member of the crew who was already actively pursuing his dreams before meeting Luffy (one could argue that Robin had as well, but seeing as she was borderline suicidal when she joined the crew, Zoro feels he could win any such argument without too much bother). He was already a strong warrior working steadily towards his goal. He already lived in the moment with no regrets, and he didn't let any demons haunt his past.
In many ways, Zoro was ready and waiting for Luffy while the others had to be molded. Zoro had advanced as far as he could in the East Blue. Even if he kept finding more skilled opponents, they could never truly test and advance his skill as the ones he fought with Luffy did. He was ready for more even if he didn't know it.
Although he sort of did know it. He and Luffy had always sort of known each other in a way that neither could ever hope to explain (the closest anyone had come was when Nami questioned Zoro about how he always seemed to know what Luffy was planning and the captain answered himself: "Because he's Zoro! And I'm Luffy!" and then he grinned like that made everything clear, and not even Nami could argue).
Zoro thinks he was ready and waiting because his dreams aren't enough. They were enough to keep him going, enough to keep him afloat, but not enough to actually get anywhere. He would have been forever doomed to being merely Pirate Hunter Zoro of the East Blue, his potential forever unrealized.
Because while the dream of being the world's greatest swordsman is great, it is also very distant. Zoro always knew that in the back of his mind, and it was only confirmed when he faced off against Mihawk that one time. Zoro dreamed big, and he was on his way – but it was still so immeasurably distant, not quite real, whereas Luffy –
Luffy's dreams are not dreams, and that makes all the difference. When Luffy speaks to Zoro – when he smiles that huge smile with no trace of doubt or hesitation on his face and says, "I'm going to be the next King of the Pirates!" – he is not telling Zoro of an ambition or a dream. He's stating a fact, and Zoro can't help but believe him entirely, each and every time.
Luffy's dream is not a dream, and that's why Zoro is going to do all he can to make it come true. It's what allows him to make his way towards his own ambitions, and at the same time it is what makes him willing to throw them all away.
When Zoro stepped into that bubble on Thriller Bark, he was sure he was going to die. And he deserved to, if his Captain could be that injured from protecting them. If it would save Luffy, then his life wasn't even worth considering for an instant.
Zoro is the embodiment of the best first mate now. He lives for Luffy without resentment, complaint, or even any desire to do otherwise. He would do anything for his Captain, would obey any order, would fight any foe. He loves his nakama, but if it came to it – as it once almost did when Usopp left and everyone else rushed after him – he would choose Luffy over all of them without hesitation. Zoro will be loyal until the end, and he will do anything to delay that end as long as he can. He does not question Luffy, because Luffy is Luffy and Zoro is Zoro.
So Zoro's life is fuller than it has ever been before. He is changed. He is sleepy often, and grumpy, and gets into fights with the stupid ero-cook, and he trains nonstop. He laughs and makes loud kanpai with a group of nakama that mean the world to him and he puts up with most of their antics. He also puts up with Chopper and Usopp clinging to him and hiding behind him in battles. He smiles and cares and drinks in an obnoxious manner that can at times be compared to Luffy eating meat. He owes Nami enough money that he's considering handing over the stupid ero-cook to the Marines to pay it all off, and he communicates with Luffy silently in times of need like battles, stealing food from Sanji, and running away from Nami's wrath.
Luffy goes on adventures and Zoro is there. He makes mischief on the deck of the Sunny and Zoro is there. He takes down man after man until he's fighting legends, royalty, the world, and Zoro is there. He eats so much meat that he sextuples in size and Zoro is there to roll him along the street. He falls into the ocean and Zoro dives after.
He is Pirate Hunter Zoro, but not the Pirate Hunter from East Blue. Zoro is Mugiwara's Pirate Hunter, Luffy's man. And he doesn't quite hate the name anymore because whenever he hears it he is reminded of the past and how the future will without a doubt be.
One day, Luffy is going to be the Pirate King. That is unquestionable. All Zoro can dream for is to still be his swordsman. He wants people to see the two of them together, to whisper to themselves, to tell each other to watch out.
Look there, they'll say in hushed tones as Luffy laughs to the world, it's Mugiwara no Luffy, the Pirate King.
And always next to him Zoro will stand, hand on his swords and fond eye on his Captain. That's Roronoa Zoro, they will whisper next, Pirate Hunter Zoro, the greatest swordsman in the world.