It's all about immersion. You need to make things realistic from an internal logic point of view. I agree with both mwo and Sara Costa, but the point they both miss is immersion.
Let me give you an example. Your story is set in Feudal Japan, your main character is Japanese. Her name is Jane Doe. Do you see something wrong with this?
The name must make sense in the context of what the parents of the character would want to name their child. It's a wish of sorts for their child. Sometimes it's about letting them stand out; "I'll call you Mahlahkhai! So no one can read your name and confuse you with someone else." Sometimes they want the child to carry on the family legacy; "John Baptiste VIII, it's a family name." Sometimes it's cultural; a French boy named Jacques, and his sister Fleur. Sometimes it's time related; Dale being a girl's or boy's name dependant entirely on when the name is given (as an example, because I have a male cousin named Dion, and a female cousin, his sister, named Dale).
Figure out what the common thread would be of the time, and either consciously go with it, or consciously go against it. Even if the reasons for either are not readily apparent.
As another example, from my own story I'm working on. Fraternal twins, brother and sister, are named Ina Miyo (Ina being the family name, given their mother is Japanese), and James Tessier (Tessier being the family name, given their father is French/Arabic). There's so much being revealed about them via their name, for so many reasons. But these aren't reasons that are readily apparent, they are delved into one step at a time.
So what do the fictional parents want this child's name to say about them? That they fit in with their peers? That they were destined to stand out? And to build on Sara Costa's point, their handle name (or nickname) is also very important. That is a conscious choice by someone to see this person in this light.