Do you only want to change the name of the content type visible for the editor? For example from "Start Page" to "My Super Start Page"?
If so just change or add the DisplayName property according to http://world.episerver.com/documentation/Items/Developers-Guide/Episerver-CMS/9/Content/Attributes/

If you want to change the class name that represents your StartPage, I hope that you have added a GUID to your ContentType attribute.
If not, look in the tblContentType table in your database for the row that represents your StartPage. Copy the GUID and add it to the GUID property of ContentType attribute.
After that you only need to change the class name of the Page Type. Episerver will understand that you have updated the Page Type as the GUID is the same as earlier.

If you only want to change the name of your Start Page in the page tree, there's nothing preventing you to just change the name as all references to content in Episerver are using ContentReference or PageReference (wrapping the id to the content).

If you have already created your new Page Type and want to convert your existing start page to the new one, use the Convert Page Type function in admin mode - http://webhelp.episerver.com/14-1/EN/#EN/CMS Admin/Admin_ConvertPages.htm%3FTocPath%3DAdministering%2520the%2520website%7CContent%2520types%7C_____1

You can it like this using Migration class

public class Migration : MigrationStep
    {
        public override void AddChanges()
        {
ContentType("NewStartPageName").UsedToBeNamed("OldStartPageName");
        }
    }

Hope it helps!

Gayathri

If you want to change so that the code looks like it had the correct name the first time you wrote it, migrationsteps will only add extra code

By the way I found how you can see the Content Type GUID without going to the database

• Go to admin mode, click the tab "Content Type" and find your page type.
• Click the button "Information"
• In the box "Advanced" you'll see the Content Type GUID

Thanks @alif