No, not that I remember. When you save-as an assembly file in Inventor, it only gives you the option of naming the assembly file. You have to rename the part files the old fashioned way.
In the SAVE AS dialog you can rename the main assembly and all the parts in it. When it first opens you can select a new folder location or select one from the dialog. To rename a part double click on the part name and rename it, when you TAB out of the name field it will indicate a New part. It just takes some time and I think you need to select the SAVE ALL AS option.