You can register the new domain and then delete the old when ready. You do not have to build a new site. Unfortunately, search results are based on the URL, so if you simply delete the old domain, you will lose the search results you have built up over the years. You may want to keep both and redirect the old domain to the new. Over time that should balance out the rankings to the new domain and make sure you don't toss away the old results. If you are concerned with search rankings, then just delete the old. It is not possible to change a domain name.