Hollywood was not named for holly growing in the hills. The name was borrowed from a house in Illinois.
In the 1880s, Harvey Henderson Wilcox and his wife, Daeida, owned ranch land near Los Angeles. They planned to turn it into a town. Daeida heard the name Hollywood from another traveler, who owned an estate by that name in Illinois. Britannica says she heard it on a train. She liked it and passed it on to her husband.
Her own explanation was short. "I chose the name Hollywood simply because it sounds nice," she said, "and because I'm superstitious and holly brings good luck."
The name went on the paperwork in 1887. Sources give slightly different dates. Wikipedia says Wilcox bought 120 acres on February 1, 1887, and filed the Hollywood map that August. Either way, the name was in place by the end of 1887.
A persistent local story says the town was named for toyon, a native shrub also called California holly, which grows on the nearby hills. The Natural History Museum of Los Angeles County calls this a myth. Toyon did get a consolation prize: in 2012 the city made it Los Angeles's official native plant.
Hollywood began as a quiet settlement. It incorporated as a city in 1903 and merged with Los Angeles in 1910. That same year, D. W. Griffith shot In Old California there, the first film made in Hollywood. Nestor opened the first permanent studio in Hollywood in October 1911. By 1910, Etymonline notes, barns were being turned into movie studios.
The place name soon became a name for the business. Etymonline dates "Hollywood" as a word for the film industry to 1922, and for American movies in general to 1926. The sign in the hills went up in 1923, reading HOLLYWOODLAND, as an advertisement for a housing development.
The name then became a pattern. By 1977 the Indian film industry in Bombay, now Mumbai, was being called Bollywood. A borrowed Illinois estate name now labels film industries on the other side of the world.