Your photography business name - or any business name, for that matter - is one of the most important early decisions you'll make. Choose a poor name and you'll steeply reduce income possibilities. Pick the right name, though, and you'll find more clients and more work.
As you consider your possibilities, keep in mind that your business name should work for numerous marketing activities. The name should look nice and neat on a business card, be easy to pronounce and spell, and translate into a usable website domain name.
Keep it simple. Many photographers use their names to denote their business name. This makes it very easy for potential clients to identify you and also find your online website or portfolio. However, if you have a very common name (e.g. John Smith Photography), your business name will be easily lost in a crowd.