Names. Who is that character? You know...the tall one with the big nose and says things that make you laugh out loud. What's his name? Okay...now is that the right name? Names. They'll get you every time.
I name my characters first, then I flesh them out. I discovered years ago that if the name is wrong, nothing else falls into place no matter how hard I try. If the name is right, I can hear the character's voice. The wrong name is like putting a rubber nose on the Mona Lisa. Amusing, yes; but ultimately not so good an idea.
I have changed characters' names as I've slogged through the editing process - usually because I've discovered that I've named characters with remarkably similar names or have six characters with names starting with the same letter. The advantage of naming at that point is that I know the character intimately as opposed to naming him/her at the beginning of the process when I have nothing more than a passing acquaintance.
There is also the situation of beginning your first draft with sweet Polly who makes tea and reads Jane Austen under her blanket every night who by the end of the draft has revealed her true Machiavellian nature and her propensity for high-stakes card games.
Do you change her name to give a hint of her true nature? Some writers will, some won't. Personally, I won't.
I admit I am somewhat sensitive about names - having spent a lifetime (and I'm really not exaggerating) explaining to people how to pronounce my own. There was an email that has made several rounds demonstrating that most people only read the beginning and end of a word and that the middle could be gobbledegook. This explains why I have answered to "Elizabeth" all my life. Nothing wrong with the name, it's just not mine. Mine is the Scottish version (which is interesting because I'm not Scottish).
Sorry, I seem to have digressed...
When do you name your characters?