I generally keep the default names in most cases, but there are a few exceptions, especially in some of the PSOne FF games, where I'll change the default name out for, say, a real name not mentioned until later in the game, or one that's secret. Examples (spoiler): (SPOILER)

In FF7, I change Red XIII to Nanaki (after his real name), and Cait Sith to Reeve (after the Shinra employee that controls him).
In FF9, I usually change Dagger back to Garnet or Sara (after her real name) when I get the Namingway card, and sometimes Steiner to Rusty (after Zidane's nickname for him). I also changed Amarant to Coral in one of my early games, but I decided I liked Amarant better).