It is possible to add custom media size in admin media edit?

add_image_size( 'medium-something', 480, 480 );

// Register the useful image size for use in Add Media modal
add_filter( 'image_size_names_choose', 'your_custom_sizes' );
function your_custom_sizes( $sizes ) {
    return array_merge( $sizes, array(
        'medium-something' => __( 'Medium Something' ),
    ) );
}

Be aware that if the size does not already exist for an image, it will not be an available option in the dropdown. New image sizes are applied only to new uploads without regenerating thumbnails for all existing images.