Firstly, you need to check if the word is a trademark. Check it here: http://tess2.uspto.gov/
If this is already a trademark, don't register domain even it's available. Also don't register domain containing this word. The trademark owner can claim your infringement of trademark and get this domain back from you.
Now, if there is no trademark, you can start to check domain availability. Note: If you obtain this domain before others register this word as trademark, they can hardly claim your infringement and get domain from you.
After getting the domain, optionally you can continue to get the trademark if you have strong vision. A trademark could protect your business name, including preventing others using similar name(say a domain containing your word). You can ask an attorney to help. This will cost hundreds to thousands dollars depend on your classes. http://www.uspto.gov/web/offices/ac/qs/ope/fee100512.htm
The above is for trademark. For famous person, it's similar.
" So, if somebody registers a domain name that contains a celebrity’s name that’s identical or confusingly similar to that celebrity’s name, so , for example, a typosquat what we call a typosquat which would be a short typographical error of a celebrity’s name, then that party can seek up to $100,000 per domain name and a recovery of the domain name" -- Source: http://tcattorney.typepad.com/domainnamedispute/2010/03/celebrity-cybersquatting-trademarks-domain-names-cybersquatting.html
In general, if you register the domain as famous person's name and want to utilize his/her influence, which is likely in your question, you will have trouble. If not, he can still argue it. So, better not to do that.