First of all, you need a new logo in PNG format, it can be any image. Then place it in UI/ folder inside assets/ folder. It must be like assets/ui/your_image.png.
Then go to assets/scripts/p_mm.gd, this is a main menu script file, there is a _menu_init(mm) function, in the end of this function put this code:

That's all, now you can start the game and see that your menu background is changed!