All the information required to change the logo can be found in the source code, assuming you understand what's going on.
It won't be easy to do as a non-programmer, since you must convert the image to the proper format then recompile DOSBox to achieve what you want. You could edit the binary in a hex editor, but you'd need to find an image that compresses to exactly the same size as the current logo (or perhaps a smaller one would be ok too?), and it would be painfully long to do, anyway.
I don't think you'll get more help than this here, because the splash screen is there to prevent random people from using DOSBox stealthily, for example bundled with an DOS program that they would want to sell without acknowledging the authors. We don't want to make that process easier for them.