Summarize:

A stage name can help you accomplish a number of things, which all can influence how you decide on your name. Branding: A stage name can help you brand your performance persona, giving you a separate identity to develop as a brand. Separation of personal and professional life: A stage name will be a very public name, possibly a household name. While some people might still know your real name, keeping your real name separate from your stage name can afford you some level of privacy. Differentiation: If your real name is very common, a stage name can help you stand out and be more memorable. Prejudice considerations: Some people have used stage names in the past in order to decrease immediate reactions of racism, anti-Semitism or other forms of prejudice. Luckily, this is less often the case today. Similarly, some women may have avoided a hyphenated name because it might indicate they're married, which unfortunately some consider to be detrimental to their careers. Your stage name is a way to express yourself. What do you want your name to signify? Think about how a stage name might be able to channel your performance persona. Whatever your stage name, people will likely want to know how you decided to call yourself that. If it's an uninteresting story, then perhaps think about making up a more exciting story to go with your name. Look online and in name books to learn the meaning of the name you've chosen. Learn the history of the name. Does the name's meaning and history reflect what you want it to mean? Think about how people can find your name through search engines like Google. If you use very common words, especially single words like Trouble or Heart, it may be hard for fans to find you online. There can be the appeal of choosing a name that reflects the moment, where you might follow a fad. Also consider where you want to be in 10 or 20 years. Does your stage name suit an older performer just as well as a younger one? Child performers should consider how their names will grow with them as they get older. Joe Yule called himself Mickey Rooney, a good name for a kid actor. But it was less useful as an adult actor. Similarly Lil' Bow Wow had to drop "Lil" when he grew up. Choose a name that you won't get tired of quickly. If you think you might hate your stage name in six months, think of a different moniker.
Understand what a stage name can do for you. Choose a name that reflects your persona. Have a story behind your name. Do research about your name. Choose a searchable name. Choose a name that will grow with you.