Display random image url from list of input values

Instead of echoing out these images, just store them as strings inside an array and choose one of the array items at random.

<?php $headerimage_options = get_option('headerimage_options' ); 
$images = array();
$images[] = '<img title="'.get_bloginfo('name').'" src="'.esc_url( $headerimage_options['image'] ).'"/>';

$images[] = '<img title="'.get_bloginfo('name').'" src="'.esc_url( $headerimage_options['image2'] ).'"/>';

$images[] = '<img title="'.get_bloginfo('name').'" src="'.esc_url( $headerimage_options['image3'] ).'"/>';

$v = array_rand($images);
echo $images[$v];