Suppose I have an existing site and I want to change the domain name without changing hosting.
I could set up a 301 redirect from the new site to the old site, but that doesn't actually change the name, it just redirects.
I could set up new hosting and actually move the site to the new host with a 301 redirect from old to new, but that means paying for new hosting which I'd like to avoid since I don't actually need two sites running.
What other options do I have?
Set up your new domain so that it points to the old content. If you do this properly you should be able to pull up the content with both domains. Then you'll want to do a 301 redirect from the old URLs to the new URLs. This will tell both your users and the search engines that your content has moved to a new domain and to "forget" about the old domain. The 301 redirect will also help you keep your rankings for pages as it does transfer over link juice, etc.
You can do one of the following
