I’m totally new to WordPress and WooCommerce, so apologies for the poor explanation.
I have this code:
$text = apply_filters( 'prefix_xml_feeds_productname_variant', $text, $product_item->ID, $vars->ID );
And need to display $vars->ID in my function:
So I got:
function custom_product_name() {
    global $product;
    
    $product_name = $product->get_name();
    $sku = $product->get_sku();
    
    $text = 'Example.com ' . $sku . ' ' . $product_name . ' ' . $vars->ID;         
    return $text; 
}
add_filter( 'prefix_xml_feeds_productname_variant', 'custom_product_name' );
How can I access $vars variable value in my callback function?
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Answer
As you can see apply_filters( 'prefix_xml_feeds_productname_variant', $text, $product_item->ID, $vars->ID ); contains 3 parameters
So you could use it like
function custom_product_name( $text, $product_id, $vars_id ) {
    // Get product object   
    $product = wc_get_product( $product_id );
    // Is a product
    if ( is_a( $product, 'WC_Product' ) ) {
    
        // Get product name
        $product_name = $product->get_name();
        // Get product sku
        $sku = $product->get_sku();
    
        // Output
        $text = 'Example.com ' . $sku . ' ' . $product_name . ' ' . $vars_id; 
    }
    
    return $text; 
}
add_filter( 'prefix_xml_feeds_productname_variant', 'custom_product_name', 10, 3 );
More information: https://docs.woocommerce.com/document/introduction-to-hooks-actions-and-filters/
Using filter hooks
Filter hooks are called throughout are code using apply_filter( 'filter_name', $variable );. To manipulate the passed variable, you can do something like the following:
add_filter( 'filter_name', 'your_function_name' );
function your_function_name( $variable ) {
    // Your code
    return $variable;
}
With filters, you must return a value.