First change the header image size in your functions.php file to the exact size of your image, and then you’ll be able to upload without cropping the image.
It should look like this –
//* Add support for custom header
add_theme_support( 'custom-header', array(
'width' => 360,
'height' => 164,
'header-selector' => '.site-title a',
'header-text' => false,
) );