I'm going to do my best to explain this as plainly as possible, as I've been typing and deleting for some time now, trying to get this explained. haha Within my novel, I have two characters, originally, Ariane and Analise. The two have known each other for quite some time and are intimate friends. However, after a series of events, the two come to be known by different names - Ariane becomes Imogen, and Analise becomes Elsie. Now, my story doesn't start until well after they take on these new names. The novel is also told from multiple (first person) perspectives. My issue is this: While the story is being told from any of the other three main characters, the characters are referred to as Imogen/Immy and Elsie, in dialogue, as well as in narration. However, naturally, the two women refer to and think of one another as the names by which they originally knew each other. I feel like it would be jarring/confusing to readers to have Elsie suddenly become Analise because it's Imogen's chapter, but, at the same time, it would be unusual for her to refer to her friend, even internally, as another name than what she's always known her by. Any opinions/suggestions for how to keep the old and new coherent with the changing perspectives?
I would try to stick to one set of names as much as possible, and maybe just throw in references to the effect of (from Imogen's POV) sometimes Elsie would say something, a particular word or a phrase, and I would suddenly be transported back to a time when I knew her as Analise.... If you constantly switch names no-one is going to have a clue who is doing what though.
I recently had the pleasure of reading a manuscript in which all of the characters had two names, that the other characters, and narrator, would switch around at their own pleasure and discretion. There were many reasons that the story was awful and that's probably in the top five. Having seen it used, I would strongly recommend against it. I understand why, you you're readers will understand why, but understanding will not make them less confused when they encounter it.
I would seriously reconsider whether you absolutely need to do this. It is easy enough to confuse readers -- this is going to lose a few. (Heck, some readers get confused even when you have two or more characters whose names start with the same letter.) Make things as easy as possible or you're going to lose some.
You should try to find a way to keep the names of characters as simple as possible and switch between them as little as possible. If the characters are in contact after the name change I would think that at some point they would switch over to using the new names so you could get away with using the new names exclusively. If they are no longer in contact you could simply have them refer to each other with their original names but not mention that Analise and Elise are the same person until the two friends come into contact again. Once the characters were reunited I would have a short period of "Analise-no Elise" before switching to the new name. Is it necessary that both characters have new names? I would suggest getting rid of one if not both of the aliases.
I guess I misread the names. It isn't really a problem if I keep reading Elsie as Elise unless there is an Elsie and an Elise or I start discussing the character with other people.
Why? I do get the idea, they have always known each other by those names, it would believable that they would continue using them. However, that doesn't mean it would be unbelievable if they adopted the new names rather quickly. You say it takes place "well after they take on these new names," I don't think you are giving these people enough credit if you think they would still be using their depreciated names at this point. Although, if they have been away from each other all this time they may not have had time to adapt, but either way I doubt anyone would call you out for having the characters learn to refer to each other with their new names fairly quickly. So yeah, have to agree with the general consensus here. It really isn't worth confusing the reader.