Typically, you would open the drawing, which opens the model, and rename the drawing. If you rename the drawing in-session only, the original will not be over-written. You would do the same to the part/asm file while the drawing is in session. You will see that the new model name is part of the drawing now.
If you want to make sure nothing bad happens to your original files, it may be better practice to make a temp folder; make sure nothing is in Creo memory; change to the temp folder as the working folder; open the drawing; open the part/asm; rename the part; save the part; rename the drawing; save the drawing.
However, there are tricks to making drawings save as a new drawing with save-as for a part or asm. I do not know if save-as mirror has this capability but would be nice if it could.
Welcome to the forum, Paree.
