I'm trying to achieve the gradient effect shown in the below examples on each letter of the type I'm using in a logo design. I don't really know what this style is called, so I can't effectively look for tutorials regarding how to do this. Can someone point me in the right direction?
They're just careful applications of gradient fills and/or meshes to give a depth effect.
Not everything has a specific term for which complete tutorials can be found.
I would advise just trying to recreate these logos and come back when you hit a specific problem.
One good, quick, highly flexible and non-obvious way of getting effects like the first one would be to create a gradient-like blend object from a few thick-stroke lines (see below), make a new pattern brush from it using the brushes panel, curve a path or paths into the right shape, and apply the brush to the paths. Here's an example:
The original blended object is top left, the three elements used to make the blend copied and released top right. Note it has to be a blend not a gradient fill since illustrator can't use gradient fills in brushes.
They almost certainly didn't use this technique. But it's a good one :-)