No. The business has to be served through its registered agent for service of process. Luckily, that's public information, and readily accessible at the California Secretary of State's website, www.sos.ca.gov. Look for the "business search" page.
Serving the business directly is an option. However, serving the registered agent for service of process, if you can determine this person, is the preferred choice. Here is a link to the California secretary of state website you can use to determine the registered agent for service of process: https://businesssearch.sos.ca.gov/
If the business is not listed, they may be using a fictitious business name, which would require you to locate the fictitious business name as registered the county registry (most counties now provide online searching), and determine the registered owner of the fictitious business name. If your findings indicate the owner is an entity, use this entity in your search on the CA secretary of state site; if none, just serve the business directly.
My colleagues did not mention - a plaintiff cannot serve his own summons and complaint. Has to be an adult over 18 when then files a proof of service.
The above is general legal and business analysis. It is not "legal advice" but analysis, and different lawyers may analyse this matter differently, especially if there are additional facts not reflected in the question. I am not your attorney until retained by a written retainer agreement signed by both of us. I am only licensed in California. See also avvo.com terms and conditions item 9, incorporated as if it was reprinted here.
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