In the book we learn that
Lorna Doone isn't actually a Doone.
So I was wondering, couldn't they have come up with a better name for the book? Or was the whole theme of the title supposed to be a mystery?
This entire answer is a spoiler; it's impossible to answer the question without it. (Even the question doesn't make sense without the spoiler.)
Lorna Doone has 75 chapters in all. The secret of the eponymous heroine's identity is not revealed until Chapter 53—more than two-thirds of the way through. When John Ridd first meets Lorna in Chapter 8, the alert reader will probably suspect that this is the little girl he has seen briefly in Chapter 3 at an inn, who in turn is the same little girl he notices being kidnapped by the Doones later in that chapter; otherwise, those are loose strands in the narrative. But the point is not dwelled upon until the spoiler is revealed.
The lawless Doones exercise tyrannical control over Exmoor. Since Lorna is raised among and by the Doones, everybody assumes that she is one of them. She is also expected to marry another of the Doones, her putative cousin Carver. Additionally, the Doones have murdered John's father. The crux of the novel is that the love between John and Lorna is forbidden precisely because he is a Ridd and she is a Doone.
Even before her true identity is known, John manages to rescue Lorna from the Doones and take her to live with his family. This rescue's narrative force and emotive effect depend on the feud between the two families. If Lorna weren't allegedly a Doone, her running away with John would read very differently. His being a Ridd wouldn't complicate matters for him, as it would be a straightforward act of rescuing a kidnap victim from his enemies, the Doones. There would be no conflict for her either, as she wouldn't be bound by her sense of loyalty to the Doones or love for the man she thinks was her grandfather.
When Lorna is revealed to be an heiress, it becomes clear that the Doone's insistence that she marry Carver was a ploy to gain legal control of her money. But while this revelation frees Lorna from any family obligation toward the Doones, it also comes in the way of her and John's love, as she is far above his station. The legal formalities of establishing her true identity and, along with it, her claim to her fortune also separate her from John. The unraveling of these tangles occupies the last third of the novel, along with several melodramatic twists (for example, Carver's near-fatal shooting of Lorna when she and John are actually at the altar on their wedding day).
Given how important Lorna's identification as a Doone is to the entire novel, no other title would make as much sense. Calling the novel "The Doones" would be misleading, as the novel is specifically about Lorna. The Doones matter only insofar as she is taken to be one of them. Calling it "Lorna Dugal" (her actual name) would be a giveaway. Calling it simply "Lorna" would obfuscate the clear distinction between the Ridds and the Doones that drives the plot.
Finally, it should be noted that the Doones, John Ridd, and the highwayman Tom Faggus (an important character in the novel) were all legendary Exmoor figures from the 17th C., whose stories R. D. Blackmore drew upon in writing his novel. The title Lorna Doone would immediately link his novel with those legends. No doubt Blackmore wanted his heroine to be part of the notorious Doone family while still being a blameless figure, and the plot twist about her identity helps him achieve that goal.