First you must remove all physical traces of the boat's old name. Take the old log book ashore, along with any other papers that bear the old name. Check for offending books and charts with the name inscribed. Be ruthless. Sand away the old name from the lifebuoys, transom, top-side, dinghy, and oars. Yes, sand it away. Painting over is not good enough. You're dealing with gods here, you understand, not mere dumb mortals. If the old name is carved or etched, try to remove it or, at the very minimum, fill it with putty and then paint over. And don't place the new name anywhere on the boat before the denaming ceremony is carried out. That's just tempting fate.
How you conduct the ceremony depends entirely on you. If you're the theatrical type, and enjoy appearing in public in your yacht club blazer and skipper's cap, you can read it with flair on the foredeck before a gathering of distinguished guests. But if you find this whole business faintly silly and embarrassing, and only go along with it because you're scared to death of what might happen if you don't, you can skulk down below and mumble it on your own. That's perfectly okay. The main thing is that you carry it out. The words must be spoken.
There are two things to watch out for here. Don't use cheap-cheap champagne, and don't try to keep any for yourself. Buy a second bottle if you want some. Use a brew that's reasonably expensive, based on your ability to pay, and pour the whole lot on the boat. One of the things the gods of the sea despise most is meanness, so don't try to do this bit on the cheap.
What sort of time period should elapse between this denaming ceremony and a new naming ceremony? There's no fixed time. You can do the renaming right after the denaming, if you want, but I personally would prefer to wait at least 24 hours to give any lingering demons a chance to clear out. (Scroll down for the wording of the ceremony.)
Afterwards - Now you can pop the cork, shake the bottle and spray the whole of the contents on the bow. When that's done, you can quietly go below and enjoy the other bottle yourself.