Extrude help

I have a simple question I think.

When I extrude something how can I name each object differently? When I extrude it becomes one object then I can’t move the cubes independently. I can move them in edit mode but not in object mode.

please help

Extrude only creates additional geometry to an object, not a new object.
Sounds like you don’t want to extrude but to copy Shift+D or to separate off part of a mesh to create a new object, select the mesh and press P to separate.