To have your own website you must have a unique domain name. Thousand of domain name is being reserved everyday. So you may not get your desired domain name free that usually occurs. In case of such situation you have to choose the alternate domain name nearly relevant to you fist choice. you may use "-" between two words. Or there are many extension such as .net,.info etc available you may choose the best one that suits you best. There are many site online that provide that provide free domain name if you purchase hosting from them and offers many special offer. You may also visit their services and then take final decision.