To disable the splash screen add -Dnosplash=true in Help | Edit Custom VM Options or nosplash=true in Help | Edit Custom Properties.
It can be also disabled by running with nosplash command line option. For example, idea.exe nosplash (on Windows).
You can modify the menu/desktop shortcut to run with this parameter automatically.
There is also a feature request to make it a setting, feel free to vote.
In case you want to change the image, it’s loaded from this file:
<IDEA_DIR>\lib\resources.jar\idea_logo.png.