Is there any reason for this?
The name Hollywood was coined by H. J. Whitley, the “Father of Hollywood.” Whitely bought 500 acres from E. C. Hurd; Hurd’s wife’s friend (stay with me here), Daeida Wilcox, co-opted the name “Hollywood” from her neighbor, Ivar Weid, who lived in what was then called Holly Canyon.
According to the diary of H. J. Whitley, known as the "Father of Hollywood," on his honeymoon in 1886 he stood at the top of the hill looking out over the valley. Along came a Chinese man in a wagon carrying wood. The man got out of the wagon and bowed. The Chinese man was asked what he was doing and replied, "I holly-wood," meaning 'hauling wood.' H. J. Whitley had an epiphany and decided to name his new town Hollywood. "Holly" would represent England and "wood" would represent his Scottish heritage. Whitley had already started over 100 towns across the western United States.
2) Bollywood: 3
The name "Bollywood" is a portmanteau derived from Bombay (the former name for Mumbai) and Hollywood (in California), the center of the American film industry.
3) Tollywood: 3
Dating back to 1932, "Tollywood" was the earliest Hollywood-inspired name, referring to the Bengali film industry based in Tollygunge (in Calcutta, West Bengal), whose name is reminiscent of "Hollywood" and was the centre of the cinema of India at the time. It was this "chance juxtaposition of two pairs of rhyming syllables," Holly and Tolly, that led to the portmanteau name "Tollywood" being coined.
4) Kollywood: 4
Kollywood is a colloquial term used to describe this industry, the word being a portmanteau of Kodambakkam and Hollywood.
So basically, the "wood" part comes from the hauling wood part and everyone else formed by it by creating a portmanteau between the Hollywood and something with themselves.
They are inspired from Hollywood, Los Angeles. Wikipedia gives a full list of Hollywood inspired nick names.
Hollywood-inspired nicknames, most starting with the first letter(s) of the location and ending in the letters "-ollywood" or "-wood", have been given to various locations around the world with associations to the film industry - inspired by the iconic Hollywood in Los Angeles, California, whose name has come to be a metonym for the motion picture industry of the United States. Some of the following names, however, did in fact exist before Hollywood.
Hollywood is a real place whereas the names like Bollywood, Tollywood, Kollywood do not exist in maps. They just indicate the names of the film industries.
These nicknames are usually formed by the Nickname of the Portmanteau of the place they are located or the language and -ollywood.
Bollywood : Bombay + Hollywood. How did the word "Bollywood" originate? discusses the derivation of the how the word was formed in detail.
Kollywood : Kodambakkam + Hollywood
Mollywood : Malayalam + Hollywood
Tollywood (Bengali) : Tollygunge + Hollywood
Tollywood (Telugu) : Telugu + Hollywood
Ollywood = Odiya + Hollywood
Many industries are also nicknamed inspired from Hollywood which are found in the article linked above.