Do an Internet Search
You want to have several potential cosmetic dentists to choose from at this stage. Ideally five or more, but at least three.
However, you should do an Internet search even if you have enough candidates. Search each of the names you were given, using the word “dentist” to help you focus on results relevant to the person you’re considering. (“Cosmetic dentist” is an informal description, not an official title, and might not be helpful at this stage.)
You should find the dentist’s website, and hopefully some other results. Pay attention to these other results. In some cases, you might find a red flag that cautions you against a dentist, like disciplinary action or several disgruntled patients. More often, though, you’ll find positive results that help you decide between dentists. Community involvement, charity work, scholarly publication, graduations, and awards can all help you decide who is the best cosmetic dentist for you.