Your use of a stage name in your performances will be determined by contract, so please ensure the language in any applicable performance contracts says your credit should be attributed to your stage name instead of your legal name.
You do not necessarily need a DBA unless you will be operating your business under this stage or other fictitious name. You state that you are operating under your legal name, so that should be sufficient unless you later decide to operate as a DBA or corporate entity. You will need to get a business license under your legal name in the city or jurisdiction where you conduct your business. This is typically the address that you report on your taxes for this business activity. Please be aware that you may have multiple-State tax issues and obligations if you will be performing shows and generating monies in other cities and States. I would recommend getting a consultation with a tax and business attorney on the best way to structure your business.
Depending on the distinctiveness in your stage name, you may also want to consider filing a trademark application for your stage name in various classes at some point in the future.
The foregoing response is provided for general informational purposes only and is not a solicitation for business. Please retain an attorney if you need specific legal advice. No attorney-client relationship is established until both you and me agree to establish one, and neither transmission of information herein, nor the receipt of such information, constitutes an agreement to establish an attorney-client relationship.
A DBA is not the same as a business license. A business license is essentially a local government's way of taxing you. A DBA is a fictitious business name that allows you to enter transaction using a different name. However, a DBA provides no legal protection.
I believe you might be confusing a business license with a fictitious business name statement.
Generally, cities require businesses (including independent contractors) to obtain business licenses. Fresno is such a city: http://library.municode.com/HTML/14478/level3/MUCOFR_CH7CIFIRETA_ART10BULIENPR.html#MUCOFR_CH7CIFIRETA_ART10BULIENPR_S7-1002LIPRCORE
You will need to file what's called a fictitious business name statement ONLY IF you "regularly transacts business in this state for profit under a fictitious business name" (Cal. Civ. Code s. 17910). Fictitious business name statements are filed by county. Here, you stated that you are transacting business under your legal name. So, you do not need to file a fictitious business name statement.