There are many dialogues on whether an actor or an actress should consider obtaining a stage name. We're not talking about legally changing your name here, but only using a different name for credits during your performances.
There are many reasons why you would want a stage name. Having a difficult name to pronounce could be a leading reason. Other times names in one language may mean something completely different in another - you may not want to have attributes applied to you based on what your name is.
Another reason could be branding. If you are a comedy actor while your name has a serious sound to it, you may consider finding something cute and catchy instead. Not to mention those individuals who are born named after somebody famous, or maybe it so happens that in your lifetime somebody who bares your name became famous. Take Michaeal Keaton for instance. He was born Michael Douglas. Can you imagine having both actors with identical name?
Speaking of branding, if you are choosing a stage name consider something unique. In today's world everything is on the internet. If you pick a name "John Smith", the chances are you will never get a good Search Engine score. Simple names are great, but if they are not unique enough, researching you by name on the internet might be cumbersome or even impossible.
My last name is Mieczkowski, which is a quite common Polish name, and people in Poland would never have an issue pronouncing it, but in the United States, I have yet to come across a person who would pronounce it right without any hesitation. Is it unique? - Quite. But if I were to become an actor, I would never consider using it for credits. Name is pronounced close to "mitch-cough-ski", but I've been anglicizing it for years as "my-cow-ski", because I can see that Americans do prefer it.
One final reason I would like to add is the separation of your personal life and your business life. Having a stage name could help you feel separated from the real life. On stage you are one person, at home you are another, why not call yourself differently then. Even for that reason, were you to become famous, would you want your fans to find out everything there is to be found about who you are by just researching your name? I suppose if they are true fans, they will still find out your real name, but that's beside the point.
One other factor that I recently stumbled upon was the alphabetization. This may be more of a psychological approach rather than logical one, but someone has recently mentioned that names are often picked from alphabetized pile. In such cases having a name that starts with a Z may never get you seen. Well you must be thinking that this is what Amy Adams was thinking. Nah-ah, that's actually her real name.