I care about what I name my characters. I don't know about other writers, but there is so much in a name that I have to meticulously choose each one. Most of the time, my characters name themselves. I know that may sound like I contradicted myself, but let me explain.
When I begin a new story, the first thing I start on is the characters. Who they are, what they like to do, and what their story is.
In discovering who they are, I often start with a name.
I am American. Not that this is a bad thing, but if my character is Australian or British, I know I am probably not spelling the name how it would be in other countries. That's when the meticulous searching of names comes in. I search for alternate spellings and what the names mean in other countries, that way I will be able to ...
A) Not offend anyone because I'm making an Aussie seem American.
B) Stay true to the art of good writing.