Separating mesh into distinct objects for subsequent bolean operation

I have the shape of an eagle with a shield cut out of it which was derived from an imported SVG. I want to make the shield embossed on the eagle so I’m going to subtract the eagle shape from a cuboid. I created the cuboid using Add > Cube. The problem is that this cube appears to have just been added to the mesh of the eagle and I presumably need them to both be defined as separate objects for me to subtract one from the other. Is there a way to make a selection of nodes into its own separate object?

Excuse me if I’m not explaining this correctly; I’ve only just started using Blender although I’ve used other image editing software including GIMP, Inkscape and Google Sketchup.

Add new objects while in Object mode to make it its own separate object
Add new objects in Edit mode to make it part of the currently edited object

You can select faces of an object and separate them out to create their own object with shortcut P

Thank you very much!