What’s Up With the Title?
Okay, we’ll admit it: it’s hard not to be cheeky here. "Why is it called Mrs Dalloway?" Because it’s about someone named Mrs Dalloway, duh.
Not so fast. There’s definitely more to it than that. Think about it: Woolf could have named the novel Clarissa Dalloway or just Clarissa. But, no: the title Mrs Dalloway suggests something different. This title refers to her married name, to the fact that she’s identified with Richard Dalloway. Who Clarissa is has a lot to do with the fact that she is a "Mrs." And don't forget: "Mrs" is quite different from "Miss." Remember Miss Kilman? It’s important that she is single, and the narrator makes it pretty clear that she will remain unmarried: she’s both a lesbian (who couldn't marry back then) and sort of a people-hater.
The title also emphasizes that Clarissa chose Richard over Peter. Marrying Richard Dalloway meant marrying someone who is socially esteemed, rich, and connected. Becoming Mrs Dalloway allowed Clarissa to maintain the status she grew up with and to be the society lady she wanted to be. Plus, Mrs Walsh just doesn't have the same ring to it.
It's pretty clear that Woolf is telling us something by naming the novel Mrs Dalloway and having "Mrs Dalloway" be the first words of the novel. No need to be cheeky about that at all.