That depends a great deal on how common the names are and how well known the other book is.
I've never read "Miss Peregrine", I think I vaguely heard of it somewhere, but it's not particularly famous or iconic. And as you say, Emma, Oliver, and Jacob are all fairly common names in English. So I don't this this would be much of an issue.
The more common the names are, the less of an issue it's likely to be. Say I told you I'm writing a story where the main characters are named Henry, Thomas, and John. Would you immediately think of Shakespeare's "Henry V Part 3"? It's a very famous play, but I don't think those names would bring that play to my mind.
But it's different if you use more unusual names. If you said the main characters in your story are named Macbeth, Duncan, and Banquo, I would likely think of Shakespeare's play "Macbeth" pretty quickly.
As someone else on here noted, the combination might bring another story to mind if the individual names don't. If your main characters are named Luke, Han, and Old Ben, yeah, I'm going to think of Star Wars. But any one of those and I don't I'd think a thing of it.
If you're thinking of law: You can't copyright a name, so that's not an issue. You can get a trademark on a name, but that's a whole different animal. Trademark law is much more complicated than copyright. To claim trademark violation, you have to show that someone created confusion between your company or product and his. Like I said in a comment (before I decided to write my own answer), if you started a computer company and called it "Apple", the existing Apple Computer could sue you and I would expect them to win in a heartbeat. But if Apple Computer tried to sue a grocery store for calling a fruit they sell "apples", they would lose. Even aside from the fact that the word "apple" for the fruit existed for centuries before the computer company, no one is going to set out to buy an Apple Computer based on their reputation and advertising and think that the fruit the grocery store is selling is an Apple Computer and buy that instead.
So if you wrote a novel and called it "Star Trek" without permission from whoever owns that trademark, they could sue you. But if you wrote a story with a character named James, the fact that there's a character in Star Trek named James would not be grounds for a trademark suit.