I am trying to add current logged in user to my zoho chat

As Howdy_McGee said, you need to reference the individual data points, not the whole user object.

<?php
// Get the user object: username, email, firstname, lastname, displayname, and user ID 
$current_user = wp_get_current_user();
// Get other user meta, such as phone number
// (you'll have to check what meta_key you're using for info like this)
$current_user_meta = get_user_meta($current_user->ID);
?>
$zoho.salesiq.ready=function()
{
  $zoho.salesiq.visitor.name("<?php echo $current_user->display_name; ?>");
  $zoho.salesiq.visitor.email("<?php echo $current_user->user_email; ?>"); 
  $zoho.salesiq.visitor.contactnumber("<?php echo $current_user_meta->phone; ?>");
}