The function that's erroring on is called on a dummy CB user object to bind the post data to it so it can be used to pull the POST field value. You have something posting an input with no name is my guess, which is invalid HTML. You can add the following debug code to dump the POST data it's trying to bind.
IN: components/com_comprofiler/plugin/user/plug_cbconditional/cbconditional.php
ON: Line 791
echo '<blockquote>';
var_dump( $post->asArray() );
echo '</blockquote>';
Do you have a CB Auto Actions action or some sort of plugin/extension that's altering the post data? Try disabling CB plugins other than CB Conditional and see if it goes away. I'm unable to duplicate your issue here.