Before we get into the profound stuff, let's get one thing straight: Edgar Allan Poe liked to make stuff up. Especially women's names. Ligeia (pronounced lie-GEE-uh – nope, we didn't guess that the first time either) is just one of many he invented (along with Morella and Eulalie). It seems he just liked to make up names (as well as quotes, as you'll find out when you read "What's Up With the Epigraph?" section) that sounded cool. You could say that Ligeia, as simply an unusual name, brings a certain air of mystery to the story right from the start.
As for the big question of why Poe would name the story after Ligeia in the first place, well, that's not as easy to answer as it may appear to be. Yes, our narrator spends the whole time talking about this Ligeia lady – he is definitely obsessed with his late wife – and her return from the dead is the high point of the story. Still, this raises a difficult question: is the story really about Ligeia or is it about the narrator's obsession with her? Has his imagination turned his dead wife into something larger than life – or larger than death? There's no really good answer to the question. The most you can do is keep in mind that, even though the story bears her name, Ligeia isn't the one telling it.