You can embed text labels in the part itself or add independent text to any PCB layout. It is fiddly and bizaare like many things in F360 Electronics, so take a deep breath first.
In the PCB, simply select the TEXT tool, it is in the DOCUMENT menu in the DRAW submenu. It is hidden.
That will pull up a dialog that allows you to type text and pick some attributes. BEFORE pressing enter, use the mouse to place it on the PCB. It will likely be on the wrong layer, but jsut place it and press ENTER on the dialog box.
Once it is on the PCB, souble click the new text and the properties box will appear in the inspector pane - this is where you can selec the layer you want. After all that, you can move it to where it needs to be.
Crazy convoluted, but it can be done.
You can also right click a part and edit/add a NAME or VALUE for most parts that will appear and also move with the part. Both methods are valid, pick the one you like best.
Carlos Acosta
Factory400 - YouTube|Instagram