Generally images cannot change colors – the SVG format has some limited capabilities, but for security reasons it is not currently officially supported by WordPress (although there are plugins that force this support).
Additionally, neither the theme nor WordPress provide functionality to define multiple logo images (and then perhaps alternate between them based on specific events).
The logo image is displayed both over the static banner image and the menu bar on scroll. For best results it would need to have a color scheme that works on both these backgrounds. All three elements: the logo image, the static banner image and the header menu background color are configurable and need to be set to values that work together.