So I’m currently writing a book that takes place in Finland, though I am American and speak English. My main character’s name can be used as a play on words, and people use it to mock him throughout the story (For example, the name Adam Zapel would be pronounced aloud as “Adam’s Apple”. Something along those lines). The issue is, the word is in English, whereas in the story, everyone would technically be speaking Finnish. Should I just keep things how they are? As soon as I look to find a way to make it work in the language the characters would be speaking, the lines between translation just get blurry.
I personally wouldn't find it unrealistic that people in any country today mocked somebody for the way their name sounds in English.
I'd say keep it. I'm aware that not all countries have a capacity of speaking English as if it were their second official language, but in Denmark, it's pretty much the case. I'd believe something like this to happen in Denmark. I'd also believe to happen in Finland.
This reminds me of Life of Pi.
The protagonist is a young man from India named Piscine (French for "swimming pool". I forget why he's called this, but I'm sure he does explain it). As a kid, he was bullied at school because his name sounds like "pissing", so he shortened his name to "Pi" and made it stick by reciting hundreds of digits of pi on a blackboard.
Logically, the characters in Life of Pi (at least at that point in the book) would not be speaking English, just as those in your story would not be. But Life of Pi just ignores this issue for the sake of telling a good story. You should too.