Well it works but I'm clearly way out-monked here because I don't have a clue how! Can someone enlighten me?

The trick lies in the zero-width assertion: It will fail if none of the following optionals match anything. (It asserts no rice, but if none of the optionals match, rice is what follows.)

I guess my answer was rather on the minimalist side. So, here is a commented version. But I won't just comment the same version I made first -- what's the fun in that? This time I'll use a positive lookahead zero-width assertion, not a negative. And I'll borrow the variables from tachyon's answer, including the job description that I somehow forgot first time around.

So, here goes:

  # Note, tachyon, we need the /i modifier on each of these as well:
  my $job_desc = qr/\b national\s+security\s+adviser \s+/ix;
  my $title    = qr/\b (?:dr\.|doctor) \s+/ix;
  my $f_name   = qr/\b condoleeza \s+/ix;
  my $surname  = qr/\b rice \b/ix;
  my $repl     = 'condoleezarice';
  $text =~ s/# Zero-width assertion: One of the options must follow:
             (?= $job_desc | $title | $f_name )

             $job_desc ? # Option 1: job description
             $title    ? # Option 2: title
             $f_name   ? # Option 3: first name

             $surname    # Surname -- not optional
            /$repl/gx;
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(If the surname could match any of the optionals, this would not work. Neither would the negative lookahead, though it would fail differently. But that is a problem I'll face no sooner than I need to.)

Update: Turns out there is an implied grouping with qr//, so I have removed the explicit grouping from my code.