If the "Group similar taskbar buttons" box is checked (default) and space starts to get tight on the taskbar, then then the taskbar will group together buttons represending windows from the same program and give them a common name. Where does this common name come from?

The name for grouped taskbar buttons comes from the version resource of the underlying program. You can view this directly by viewing the properties of the executable program and looking on the Version tab.

To set this property for your own programs, attach a version resource and set the name you want to display as the FileDescription property.