The address decides which office reviews your plans.
Inside the City of Los Angeles, the Department of Building and Safety (LADBS) reviews plans and approves permits. Simple projects that need no plan check can get an express permit online. Simple projects that do need plan check can be approved over the counter. Other plans go in through ePlanLA, the City's online plan review. Palisades fire rebuilds run through LADBS, which keeps a dedicated permitting and inspection support center at 16925 Marquez Avenue in Pacific Palisades. Brentwood, Bel Air, Hollywood, Silver Lake and the other neighborhoods on our service areas pages inside the City follow this path.
In unincorporated Los Angeles County, and in the cities that contract with the County, the permit comes from the Public Works Building and Safety district office that serves the address. Altadena is an unincorporated community of the County, so an Eaton fire rebuild there is a County permit; the County opened the Altadena One-Stop Permit Center at 464 West Woodbury Road, Suite 210, Altadena, with the departments that approve rebuilding plans under one roof. Simple work that needs no plan check can be issued as an express permit. Inspection requests for unincorporated County projects go in online; the County no longer takes them by phone or voicemail.
Your own city. Beverly Hills, Santa Monica, Malibu, West Hollywood and Culver City are their own cities and review their own permits. West Hollywood's Building and Safety Division, for one, issues the building permit for a kitchen remodel and the trade permits ride on it. The Beverly Hills and Malibu pages on this site walk through those two offices; the West Hollywood kitchen page covers that city's remodel path.
A County permit has a clock on it. It expires if work has not started within 12 months of issue, or if work stops for more than 180 days at any point after it starts. On a stalled job, that date matters; see when a rebuild stalls.