To add the NameMapping project item used in a project to a new project, simply add the NameMapping.tcNM file stored in the NameMapping subfolder of the project's folder to the new project using the 'Add Existing Item' item of the Project Explorer context menu. Please see the 'Sharing Project Items and Their Child Elements Among Several Projects' and 'Adding and Removing Project Items and Their Child Elements' help topics for details.
Please note that a TestComplete project can have only one NameMapping project item. Thus, the error you get is caused by the fact that you tried to add the NameMapping.tcNM file to the project that already had the NameMapping project item. Currently, you cannot import NameMapping data to an existing NameMapping project item.
I've said this before, but hey why not say it again.
TC really needs to support a more modular concept of NameMapping files. I've worked on projects where too many people needed simultaneous edit access on the NameMapping file and it just isn't feasible. The files are too difficult to merge using a diff tool.
It's really a shame because there is a lot of good functionality in NameMapping.