If you only need to change the name of the file and not the file type, simply leave the extension alone when renaming. My guess from what I read in your post is that you have something like this:
mypicture.jpg
and when you rename, you are altering the extension (meaning the three letters to the right of the dot). Those three letters tell the computer/software how to handle the file, if they are altered, Windows will throw that error about the file becoming unstable at you. SO the result would be:
newpicturename.jpg
You may know this already, so please excuse me if my interpretation of what you are asking is incorrect. If you do need to change format, Irfanview is very nice for doing that, I agree with Bichur.