If you are considering to moving to a new domain name, then you should make sure to properly redirect your page. Depending on the level of access you had at the old domain, this may or may not be easily done.
Just about the only place where it would be a problem, is if you where using a limited hosting solution for your old domain. Some hosts will not allow you access to server-sided scripting, htaccess, or server configuration files. It is very common for shared hosting solutions, to disallow access to server configuration. Most do however allow you to edit and place .htaccess files, which can be used to change the configuration on a per directory basis.
In any case, if you are unsure about how your host allows you to redirect your pages, you'd best contact them and ask. This Article will only inform you about why you need to redirect, and how you can implement your redirects.
Why you should redirect your pages
The simple answer is that Search engines will know that you moved the pages, and they will be able to update their index with the new location for your pages – the same goes for entire domains. But it is also useful for your visitors, as they will be automatically redirected to the new location in their browser.
How to redirect your old domain to a new domain
You need to use what is referred to as a 301 redirect, this can be easily implemented if its possible for you to place a htaccess file in the server-root directory – which is a common way to implement redirects. The below are some Tutorials on how to perform redirects.