I'm not familiar with any specific name that technique has, and, really, it's a rather subtle thing that I wouldn't call a distinct technique in itself.
You may hear this variously described as having a "darker" tone, or sometimes as being "throatier". What these singers are doing is opening up the back of the throat more (lifting their soft palate and lowering the back of their tongue to create extra space).
Notice that in both cases, they do this right when they go to a higher place in their range. Opening up like this helps give them better tone and can help them keep from going flat, or from having to flip into head voice or falsetto. This isn't the only time you'll hear this change, but it is a rather common place to do it.