Thank you for taking the time to write to us, but this is not
a bug. Please double-check the documentation available at
http://www.php.net/manual/ and the instructions on how to report
a bug at http://bugs.php.net/how-to-report.php

There is nothing said about this behaviour in the documentation:

http://www.php.net/manual/ru/function.ob-list-handlers.php

And - if I cannot trust the result of ob_list_handlers() (I cannot - it returns bogus handler names), is this function necessary at all?

This is how the engine stores callbacks names.
ob_list_handlers() has nothing to do with it. 
This functions is for debugging purposes only and there is nothing said in the docs that it should return valid callbacks.

Very strange, because object-based callbacks works fine with ob_start(). So I guess that full callback info is stored somewhere.

OK, debug purpose. But - maybe write it explicitly in documentation? "This function is for debug purposes only. Do not try to use it for manual callback execution - references will be wrong for object-based callbacks."

I'll detalize why do I say all this words. It would be great  to MANUALLY process all output buffers with their callbacks at the end of script - something like this:

foreach (array_reverse(ob_list_handlers()) as $h) {
  $text = ob_get_contents(); ob_end_clean();
  echo call_user_func($h, $text);
}

Why? Very simple: if I let the callbacks to be called automatically, I'll loose ALL errors, warnings and notices in them, because errors are suppress on standard OB callback execution. But, if I call all the callbacks manually (see example above), it's OK with errors.

I use OB callbacks very often, an there are a lot of PHP code in them (e.g. - HTML tag parsing, placeholder substitutions etc.). Callbacks is a very powerful technique, but - almost undebuggable.

Maybe extend ob_get_status(true) adding valid callback references to returned array?