Naming is both important and tricky. Breaking a large function into smaller ones only adds value if the names are good. With good names, I don’t have to read the body of the function to see what it does. But it’s hard to get names right the first time, so I use the best name I can think of for the moment, and don’t hesitate to rename it later. Often, it takes a second pass through some code to realize what the best name really is.
