Most stoves are painted with high temperature paint, which can scratch with use. I periodically wipe my stove top down with a thin layer of cooking oil to cure any bare metal and prevent rust, same as you would with a cast iron skillet. Cooking oil can smoke when curing, so be sure to have the space well ventilated during the next fire. I like the look of a worn in stove, but if you ever want your stove to look brand new again, you can repaint it with Stove Bright brand high-temperature paint.
Another useful product to maintain the finish of a wood stove is stove polish. If your stove is rusty, rubbing it with stove polish can simultaneously remove rust and add a layer of protection, while providing a shiny black finish.