Do you mean when you upload a picture from your computer? If so, then you just need to organize your photos on your hard drive a little better. There are many, many ways to do this but this is what I do. On my external HDD I have a folder called "My Pictures" (how original, huh) that I have subfolders in for anything from Photoshop doodles to hardware photos, dog pictures etc. After they are in the proper folder you can go through and do a batch rename to name them all generically like dogs01, dogs02....etc or name them individually to something that will make you remember what each one is. The good thing about the Mac Finder is that you can turn on preview so its just a matter of clicking on a file and seeing it in the Finder window without actually having to open it in another program.
Now my wife, on the other hand, loves iPhoto and the way it organizes all the photos into folders based on when they photos were taken/imported -- year>month>day and it works good for her because she can remember dates really well.
You can rename your photos whatever you want, make it easy for yourself.