Simulations linked in others comment:

https://www.youtube.com/watch?v=Tr1zDVbSjTM

https://www.youtube.com/watch?v=1agm33iEAuo

The second one is much more correct, notice how it freezes before they actually merge because they time dilate out to infinity.

If they actually froze just before the merge, they will be peanut shaped like in the video.

I'm not sure if we can measure the shape of black holes, but I'm sure everyone think they are spheres with a slight deformation due to rotation.

The algorithm choose this for me https://www.youtube.com/watch?v=fKgQYOlpxmo