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Ok, so, I am currently writing a book and 3 of my characters have the same name as in another novel. I didn't realize it until someone pointed it out to me. The names I picked are fairly common and used frequently in the real world. Is it a problem? Even though the books have absolutely nothing to do with each other? Do I have to change it for safety?

PS: The names are: Emma, Oliver and Jacob. Same names as in Miss Peregrine's Home for Peculiar Children

The answer to your question depends on how strongly the set of names is associated with the preexisting work of fiction. Not just the individual names, but the set of names together.

For example, individually Romeo and Juliet are common enough names, if you set your story in Italy. However, if you name the main characters in your story Juliet and Romeo, it would be read as a direct reference to Shakespeare's work. On the other hand, if I were to write a story about Robert and Maria, I very much doubt you'd think of For Whom the Bell Tolls. In fact, I would be very much surprised if there aren't countless other stories with the same names.

You are free to reference another literary work, that's called intertextuality. However, such references should be deliberate, not accidental. Names are one way, not the only one, and not a necessary one, for creating intertextual links.

As far as copyright goes, one cannot copyright common names. Or even sets of names. I'm not sure one can copyright names one has made up. (A character would be protected by copyright, but that would include additional attributes.) Consider, we are seeing quite a few girls named Khaleesi. In a few years, one might write a biography, or a fictional biography, or just a work of fiction, about a girl named Khaleesi, similar to how a character in Good Omens has been named by her hippie parents Pippin Galadriel Moonchild (a reference to The Lord of the Rings and The Neverending Story).

So, if you're asking about the legal aspect of things, there's no problem there, and that would be true regardless of what particular names you have chosen for your characters. If you're asking about other aspects of the issue, you should ask yourself how strongly the names are associated with the preexisting work. In your particular case, I do not believe there is a strong association. In other cases, the answer might be different.

There is absolutely no rule against it, but if your set of names crosses a certain threshold of recognizability you will have to reckon with the perceived reference to another source, intentional or not. Readers accept intertextuality and will look for a deeper meaning when they spot a coincidence like this.

The more unusual any given name is, the more attention it calls to itself and the more memorable it is. Likewise, the more widely known a specific group of names gets, the more immediately recognizable the combination will be. If a set of names is featured in a work that becomes a very widely known and popularly referenced piece of culture, they will be remembered.

The names you picked (Emma, Oliver, and Jacob) are pretty standard names, not the most common, but certainly none of them stand out as unique. As a group they're not remarkable. The previously published work that already used those names was a big enough deal to become a Hollywood production, but it is not a cultural touchstone. People watched it once, if at all, and did not dwell overmuch on the characters or their relationships. Those who read the book might have a stronger connection to it than to the movie, but there are fewer of them, and if you are not writing for the same market you'll probably have relatively little recognition. I've seen Miss Peregrine and did not make the connection, so I think you're safe from the average reader picking up on it. If you happened to hate that story, the author, or the message and wanted to be completely sure to disassociate yourself from it, you might want to change one of the names, but if you don't mind the occasional person making the leap, then no problem.

For contrast, let's say you had selected instead Bella, Edward, and Jacob. A very similar selection, even some overlap, and none are particularly remarkable names in and of themselves (Bella's out of fashion and therefore more memorable). However, this group of names permeated pop culture when Twilight blew up, not least because people picked sides on the love triangle and were constantly referencing it out of context. Even people who had never seen or read it were familiar with "Team Edward/Team Jacob" debates, and the actors were on tabloids everywhere for a long time. If you happened to choose these names for your story everyone would assume it was a deliberate reference and expect to find some thematic relevance in the work, perhaps even to discover that this is an AU fanfic. If the theme were absent, they would assume you were a massive Twilight fan. If your male characters are peers, even using just Edward and Jacob would have a significant echo of Twilight and would prime readers to expect a rivalry of some sort. The connection would be inescapable for many readers, and you would have to account for that in the text or repeatedly justify it in your discussions of the book.

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.