How do actors with a stage name handle their finances?

If anybody needs your Social Security number for a legitimate reason, give them the real one. You can add an "aka" (also known as) to your bank account to enable you to deposit checks made out to your stage name. And you can file tax returns as Jane Doe aka Sally Superstar, or whatever your legal name and stage name might be. The IRS is used to handling tax returns from people who get paid under different names.