First, you may not need to do this. You can just create a new coordinate system in ANSYS Mechanical. If you still want to move a geometry in ANSYS DesignModeler, you can do it as follows:
1. In Sketching tab, select Move > Modify.
2. Select multiple desired entities to move using Ctrl+Click. When done selecting, right-click on the background and select End/Set Paste handle.
3. Click on an appropriate point (vertex) in the sketch to set it as the "handle"
4. Click on the new (desired) location of this point.
5. Esc when done.
Try it on a simple geometry first.