Are black holes spherical during merger? I've been thinking about black holes, specifically during the final moments before two merge.  I'm wondering if black holes, or I guess more specifically their event horizons, are always spherical.  It seems to me that in the moments before two merge, their respective event horizons will be stretched, somewhat like how the Moon causes our ocean's tides. I have drawn a (poor) diagram of what I think they may look like.  Notice how the event horizons are closer to the singularity on the inner side, this is because the gravity from each black hole is in opposition.  The event horizons are further from the singularity on the outer side because the gravity from each black hole adds up.
No need to guess. There's solid research done in this field. Even Wikipedia has some info:


  As two black holes approach each other, a ‘duckbill’ shape protrudes
  from each of the two event horizons towards the other one. This
  protrusion extends longer and narrower until it meets the protrusion
  from the other black hole. At this point in time the event horizon has
  a very narrow X-shape at the meeting point. The protrusions are drawn
  out into a thin thread. The meeting point expands to a roughly
  cylindrical connection called a bridge.


https://en.wikipedia.org/wiki/Binary_black_hole#Shape

There are research papers with images showing the results of calculations of the shape of the event horizons during merger. Here's an example:



The image above is taken from this paper:

On Toroidal Horizons in Binary Black Hole Inspirals


  We examine the structure of the event horizon for numerical
  simulations of two black holes that begin in a quasicircular orbit,
  inspiral, and finally merge. We find that the spatial cross section of
  the merged event horizon has spherical topology (to the limit of our
  resolution), despite the expectation that generic binary black hole
  mergers in the absence of symmetries should result in an event horizon
  that briefly has a toroidal cross section.