Auxiliary swicht-mode-power-supply topology
Do these circuits have a specific name?


Cockcoft Walton voltage multiplier is the name. Here's a multi stage version: -



Sometimes they are loosely called voltage multipliers but that does give rise to some confusion.


  Are there any noteworthy trapdoors or design considerations when using
  this auxiliary output for such applications? E.g. can this introduce a
  negative impact on the boost stage or overall efficiency?


The forward diode voltage drop is the main limiter to efficiency but other than that they can be used for quite high powers (I've designed one for 200 watts) and they can certainly be used for generating HT voltages (50 kV for example in some X-ray machines).

Here's Dave: -