If you want to become Buddhist or a Buddhist Monk, do you have to shave your head?

Q. 15: Why do monks shave their heads?

A: When the prince who was to become the Buddha left his palace to seek a way beyond ageing, sickness and death, it is said that one of the first things that he did was to shave off his hair and beard and put on the yellow cloth . Buddhist monks always completely shave their head and beard, showing their commitment to the Holy Life (Brahmacariya) of one gone forth into the homeless life. (In India some ascetics tear out their hair, while others never touch it so that it becomes a tangled mass.) A rule states that a bhikkhu should not allow his hair to grow beyond a certain length or time, so he will shave usually at least once a fortnight or month, sometimes more frequently. To do this he uses his razor, which is also one of his requisites. 'Hair-of-the-head' (kesa) is one of the five parts of the body mentioned in the ordination ceremony and is used to recollect the true nature of the body. The bhikkhu is also not allowed to dye or pluck out any grey hairs, for they are useful reminders of old-age and impermanence. (Just consider how much time and money is wasted by people trying to make their hair remain beautiful and young-looking.)

http://www.buddhanet.net/e-learning/buddhistworld/faqmonks.htm

Some Hindu and most Buddhist monks and nuns shave their heads upon entering their order, and Korean Buddhist monks and nuns have their heads shaved every 15 days.

https://en.wikipedia.org/wiki/Head_shaving

There are hundreds of millions of Buddhists in the world. If you have a look at photos taken on the streets of Bangkok or Tokyo(for example) you will see that most of them have their full complement of head hair.

https://en.wikipedia.org/wiki/Buddhism

That would seem to be the "house dress" but it certainly is not a Bhuddist core belief.

http://www.buddhist-temples.com/buddhism-facts/buddhist-belief.html