My question involves name change laws in the State of: California

I was born in the state of Colorado but have lived most of my life in California.

When I was young my Mom changed my last name by one letter because I was getting teased at school. I got my drivers license with my new name and had the name on my social security card changed when I was about 19.

Now I am trying to get a passport and the problem I am anticipating is that the name on my birth certificate will not match my license.

How is the best way to handle this? I have the documents required to petition for a a name change in my county but it is not clear to me whether this will work or what steps would need to be taken once I go apply for a passport.

Thanks in advance.