Use "Design Assistant" in manage mode. Open the iam, select all the files right click in the action cell & copy, then one at a time right click in the file name column & rename.
If you want BOTH the models & the drawings that go with them to be copied & renamed, you have to do one of the following.
1. (Safest method) Use Design assistant to copy & re-name each of the part/drawing pairs (open the idw in manage mode & copy/rename both files) Then open the idw of the assembly, copy & rename the idw, iam & ipn, then choose REPLACE for the ipt(s) that are used with the assembly & replace with the newly copied & renamed ipts.
2. Just open the idw of the assembly & copy/rename ALL of the files. Then use windows explorer to copy/rename the idws of the individual ipts. Temporarily move the original ipts out of the search path of the project file so the idw cannot find it, then open the newly copied part idws. You will get a file resolution error dialog box, use it to direct the new idw to the new part. Then move the originals back to their starting location.
If you have Vault 4, you can use the copy design function.