You could upload 10 images, one for each color of your variable product… or you could be slightly smarter and simply upload 1 “blank” image, and then when the user selects a color trigger a background color change!
Easier to code than to explain, so let’s take a look at the screenshot below (image must be a PNG with transparent background) and the PHP snippet. This could be a time-saver, enjoy!

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When yellow is selected -

When no variation is selected
PHP Snippet: Switch Featured Image Background Color On Color Variation Select @ Single Product Page
/**
* @snippet Switch Image Background @ WooCommerce Single Variable Product
* @how-to Get CustomizeWoo.com FREE
* @author Rodolfo Melogli
* @compatible WooCommerce 4.0
* @donate $9 https://businessbloomer.com/bloomer-armada/
*/
add_action( 'woocommerce_after_variations_form', 'bbloomer_switch_image_background_variable_colors' );
function bbloomer_switch_image_background_variable_colors() {
wc_enqueue_js( "
$('input.variation_id').change(function(){
if('' != $('input.variation_id').val()) {
if($('#pa_color').val() =='red'){
$('.woocommerce-product-gallery figure').css('background-color', 'red');
} else if($('#pa_color').val() =='yellow'){
$('.woocommerce-product-gallery figure').css('background-color', 'yellow');
}
} else {
$('.woocommerce-product-gallery figure').css('background-color', 'transparent');
}
});
");
}