Change featured image title and link text in WordPress

Update for WordPress 4.3+

As of WordPress 4.3, you can set the Featured Image, Set featured image, Remove featured image and Use as featured image labels to whatever custom text you’d like to use instead. You can do this when the post type is registered using register_post_type().

Here’s an example of how to to it:

/**
 * Register the Book custom post type.
 */
function km_register_book_post_type() {
	register_post_type( 'company', [
		'public'   => true,
		'supports' => [ 'title', 'editor', 'thumbnail' ],
		'labels'   => km_get_book_cpt_labels(),
	] );
}
add_action( 'init', 'km_register+book_post_type' );

/**
 * Get the labels for the Book custom post type.
 */
function km_get_book_cpt_labels() {
	return [
		'name'                  => _x( 'Books', 'Post type general name', 'textdomain' ),
		'singular_name'         => _x( 'Book', 'Post type singular name', 'textdomain' ),
		'menu_name'             => _x( 'Books', 'Admin Menu text', 'textdomain' ),
		'name_admin_bar'        => _x( 'Book', 'Add New on Toolbar', 'textdomain' ),
		'add_new'               => __( 'Add New', 'textdomain' ),
		'add_new_item'          => __( 'Add New Book', 'textdomain' ),
		'new_item'              => __( 'New Book', 'textdomain' ),
		'edit_item'             => __( 'Edit Book', 'textdomain' ),
		'view_item'             => __( 'View Book', 'textdomain' ),
		'all_items'             => __( 'All Books', 'textdomain' ),
		'search_items'          => __( 'Search Books', 'textdomain' ),
		'parent_item_colon'     => __( 'Parent Books:', 'textdomain' ),
		'not_found'             => __( 'No books found.', 'textdomain' ),
		'not_found_in_trash'    => __( 'No books found in Trash.', 'textdomain' ),

		// Overrides the “Featured Image” label
		'featured_image'        => __( 'Book Cover Image', 'textdomain' ),

		// Overrides the “Set featured image” label
		'set_featured_image'    => __( 'Set cover image', 'textdomain' ),

		// Overrides the “Remove featured image” label
		'remove_featured_image' => _x( 'Remove cover image', 'textdomain' ),

		// Overrides the “Use as featured image” label
		'use_featured_image'    => _x( 'Use as cover image', 'textdomain' ),
    ];
}

Further documentation is here:
https://developer.wordpress.org/reference/functions/register_post_type/

WordPress Versions Prior to 4.3

For sites running a version of WordPress lower than 4.3, here’s how to change/filter the featured image metabox title and link text in WordPress:

/*
 * Change the featured image metabox title text
 */
function km_change_featured_image_metabox_title() {
	remove_meta_box( 'postimagediv', 'my_post_type_name', 'side' );
	add_meta_box( 'postimagediv', __( 'NEW TITLE TEXT', 'km' ), 'post_thumbnail_meta_box', 'my_post_type_name', 'side' );
}
add_action('do_meta_boxes', 'km_change_featured_image_metabox_title' );


/*
 * Change the featured image metabox link text
 *
 * @param  string $content Featured image link text
 * @return string $content Featured image link text, filtered
 */
function km_change_featured_image_text( $content ) {

	if ( 'my_post_type_name' === get_post_type() ) {
		$content = str_replace( 'Set featured image', __( 'NEW SET TEXT HERE', 'km' ), $content );
		$content = str_replace( 'Remove featured image', __( 'NEW REMOVE TEXT HERE', 'km' ), $content );
	}

	return $content;
}
add_filter( 'admin_post_thumbnail_html', 'km_change_featured_image_text' );

To use this code, just make these changes:

Change my_post_type_name to the name of the post type for which you want to change the featured image text. Change NEW TITLE TEXT, NEW SET TEXT HERE and NEW REMOVE TEXT HERE to the new text you want to use. Change km to the function prefix & text domain of your choice.

Note: The default Remove featured image text is still visible immediately after an image is selected. The code above does not address that.