Our Mutual Friend
Our Mutual Friend takes its title from the fact that there are a whole bunch of characters in this book whose lives overlap in ways they don't even realize.
John Harmon, for example, knows all kinds of different people from different social circles, but these people might know nothing about each other outside of their connection to him. The image of John as everyone's "mutual friend" helps us think about how much we're all socially connected, even as we try to distance ourselves from one another with things like money and status.
Dickens is also being subtly snarky with this title. There's a huge hullabaloo over "marrying within one's class" (imagine us saying that in a nasal, Kristen Scott Thomas kind of accent) that goes on in this book. It's implied that you can't really know someone of a lower station (we're sticking with our accent; it's fun) and thus would do well to make a match with an equal. Really, dahling, you should stick with someone that's been properly vetted—a mutual friend, perhaps?
And this idea of "mutual friends" being the only safe bet in marriage and in business doesn't just apply to the upper classes. Remember how ticked off Gaffer is when he finds out that his son is (the nerve!) going to school and leaving poor old Pops in the dust? Yup. In the world of Our Mutual Friend, the only accepted form of networking is to stay local—and rely on mutual friends.