simply put: you cant switch the name.
Keep using the domain you have highly ranked and simply point the new domain you have to that url.
If you do want to use the new name, then you will have to do what you did to your last website - Search Engine Optimizing the pages so they are picked up, use exisitng meta tags on the new domain name, but maybe produce a carbon copy of your current site so it is under the new domain name - this way you will have 2 physical websites, both with content + high ranking in search engines
