John Harmon is a complicated cat, which stems from (paging Dr. Freud) his strained relationship with his daddy. For starters, Harmon's dad basically disowned him when John defended his sister's choice to marry a dude who wasn't so well off. But when Old Man Harmon died, he still left his money to John on the condition that John married a girl named Bella Wilfer. When John returns to London, he finds out that everyone thinks he's dead, due to a case of that perennial favorite, mistaken identity. So he decides to stay "dead" to see how things play out and to see what kind of woman Bella Wilfer really is.
But the reader doesn't know that Harmon is alive and well until a ways into the book. Instead, we're introduced to his alter ego, John Rokesmith.
Posing as John Rokesmith, Harmon shows up on the doorstep of Mr. Boffin asking to be the man's secretary. Boffin is the faithful old servant who has inherited the Harmon fortune in John's absence/death. Harmon immediately shows what a worthwhile person he is when he humbly applies to manage the Harmon money, saying,
[If] you would try me as your man of business under any name, I know you would find me faithful and grateful, and I hope you would find me useful. (3.8.111)
What a sweetheart. Harmon is being super-decent to his family servant, a move that would have been kind of unexpected back in Dickens' day. Once he's in Boffin's employ, Harmon/Rokesmith gets to work with loyalty and diligence:
On the other hand, the Secretary was discerning, discreet, and silent, though as zealous as if the affairs had been his own. (5.16.3)
Even before we know that Rokesmith is Harmon, we know that he's going to be a moral center in Our Mutual Friend. He's hardworking, kind, discreet… shucks, he probably loves puppies and can cook a chocolate cake from scratch, too.
As the plot of the novel unfolds, Harmon decides that he'll never return to life under the Harmon name, but will instead stay Mr. Rokesmith forever. Part of this reasoning comes from the fact that he thinks that Bella is a superficial woman, and everyone is better off if they think he's dead.
At a pivotal moment, we readers find out his true identity as Harmon. But this happens to be the same moment when Harmon decides never to let people know he's alive:
He took his hat, and walked out, and, as he went to Holloway or anywhere else—not at all minding where—heaped mounds upon mounds of earth over John Harmon's grave. (9.12.103)
This is symbolic earth, of course, and it shows how Harmon is letting go of his past life and moving on. After all, the woman he was expected to marry (Bella Wilfer) has proven to him that she would never love him without his fortune, and the experience has left him jaded and bitter about the whole l'amour thing.
Even after Bella sees the light, realizes that money can't buy her love, and marries him, Harmon decides not to reveal his true identity. It's weird because Bella has already proven her worth to him. But now Harmon wonders if mo' money will just bring him mo' problems. Bella realizes that something is troubling Harmon when she hears John mumbling in his sleep:
More than once, she awoke him muttering in his sleep; and though he muttered nothing worse than her own name, it was plain to her that his restlessness originated in some load of care. (19.12.6)
Yeah, it's true—Harmon is carrying a huge "load of care." He's leading a double life. Even if he has the love of a good woman, the whole secret identity thing seems to be pretty stress-inducing.
It's not until Harmon is recognized as his true self by Mortimer Lightwood that he comes forward and claims his inheritance. And guess what? That decision doesn't seem to leave him any worse off. He and Bella move to a fancy house in London and make a bunch of babies. In this case, mo' money just means mo' possessions… and perhaps an extra helping of happily ever after.