WARNING: This tutorial involves the editing of a DLL, so I suggest you backup the DLL beforehand just to be safe.
This tutorial covers modifying the prebuilt Ogre SDK. To do so, you need a resource hacker. I use XN Resource Editor which can be found here.
Once you have a resource hacker, you should look for the file OgrePlatform (or OgreMain) in your bin/release directory. Once found, open it using XN Resource Editor and then you sould see this:
The image should have a name of bitmap/106, like this:
The image should be the default Ogre logo. You can export this to change it using the Resource menu. Then you can import the image back into the DLL using the same menu. Remember to backup the original OgrePlatform_d.dll.
Note: I suggest you don't go poking around changing the DLL, just the bitmap.