I'm trying to figure out the name of this effect and how to achieve it in Lightroom or Photoshop.

I'm trying to figure out the name of this effect and how to achieve it in Lightroom or Photoshop.

You can easily recreate this effect using Topaz Clarity. Check out the bearded guy on this link.
In general, you do local and microcontrast enhancement.
The light is very specific on those photos, like the one Matt is pointing, you can try a combination of a rim light + butterfly light.
But they also have some manipulation on post.
Some styles you can explore
The two styles you can explore that comes to my mind are:
Dragan style
Tone Mapping (hdri)
Both are based on adjusting contrast, but the Tone mapping is a special manipulation of the contrast called micro contrast. This is not only a contrast on the overall image, but in adjacent zones. You can try some dodge and burn.
Some specific manipulations you can try
Contrast.
Saturation, lower it or perhaps play with a Gradient Map https://www.google.com.mx/search?q=photoshop+gradient+map.
Of course the styles can be very exaggerated or very subtle.