The name on the bag is the name you checked the bag under. You checked it under somebody else's name, so that's how it is checked.

It's water under the bridge for you, but in the future, it is critical that you double-check bag tags to make certain that they match your name and flight information. Luckily your was checked under the name of somebody in your party and to the proper destination.

To answer your specific question, it makes much more sense for the bag to be entered in WorldTracer as checked. It is far more likely that the bag tag is on the bag and that is how it will be located than that the tag has been ripped off and that it will have to be identified by other means.