Make a long list of potential names before settling on one.
Ask some friends whose opinions you trust to give honest input.
Consider using your B&B's location in the name.
If your property has a special history, consider working that into the name.
Say the name out loud several times, and have people who aren't familiar with it do the
same. Names that are hard to pronounce aren't the most useful.
Make sure it's fresh. Search for the name on the internet -if dozens of hits come up in any context, or if even a small handful of other bed and breakfasts are already using the name, throw it away.
Think about how it will look in a logo. Long names can be hard to use on brochures and business cards.
Look up potential URLs. If you want to be Smith's Bed and Breakfast, look up URLs like smiths.com and smithsbb.com to make sure a good one is available for you. And, since domain registration is relatively inexpensive, you may as well go ahead and reserve any domain name you might want in the future.
Don't forget that someday you'll want to sell the inn. Personal names (e.g. Smith's Bed and Breakfast) generally don't pass on as well as generic names.
Make sure you like the name. After all, it's your bed and breakfast!