If you're only looking to move/copy one or two tests, you can right-click on them and select "Duplicate". In the dialog box that comes up, you will be asked which project to duplicate the asset into (this works for every asset type), and you will be able to change the name and description in that project.
I don't know if there's a way to import/export from one project to another using the wizard.
I am having the same issue here. I have to move a big chunk of assets from one project into another. I looked at the exported xml file and saw the code that opened up in IE Window. However, I am not able to edit the Project Name from there. Please explain how and where exactly I should edit the target project name?