Use SolidWorks Explorer
Start > Program > SolidWorks and somewhere in there is a program called SolidWorks Explorer. This will allow you to rename and keep the associations intact.
Yes, you can use solidworks explorer to rename parts and still maintain your references. That is unless the parts you created are internal to the assembly. In which case you need right click on the part in the feature tree and "save part in external file"
Knew about SWEx but was hoping for something easier. A guy over at mcadcentral did have a somewhat better way of doing it: Open file manager, RMB on the file, select SW->Rename...
A little better that way, but I still can't do it while I'm working. It's honestly easier to open the assembly and drawing, then open the part, do a SaveAs, and then delete the old part using the file manager. I can at least rename files while I'm working instead of having to close SW in order to do it. (I also save the assy and dwg obviously.)
I think I'll have to file an enhancement request for this one.
I've always done File, Open (from inside SW) and done it from that window. Just right click then do the Solidworks...Rename... and rename it from there. I let it scan for like 2 seconds, then stop it so it doesn't scan the entire drive that I'm on since all my parts are in that one folder.
Pack and go allows you to rename your parts, if i'm not mistaken you should be able to pack and go straight into the same folder your working in. So if you pack and go from your assembly you will be able to change multiple names at once. I think this works.
I was also looking for an easier way to rename components in an assembly as I was also opening the component and using save as. However, I do have a macro that goes through each component and asks you to enter a new name. The macro renames the component in the tree only and not the name of the file. Please let me know if anyone wants to try it out.