Is there a name for the taste coming from alkaline food?
There is no single word to describe that taste, and no single taste receptor for alkaline substances either (whereas there are taste receptors for acids). 

The most recognizable taste to encounter would be "soapy". You can see it as a bit of a special case though, since it is not the taste of a pure alkaline substance, but the taste you get when the alkaline substance reacts with fats. Since most food contains fats, this is what you frequently get if you try to make alkaline food. 

You are also likely to get descriptions like "chemically tasting", since it is not a flavor we frequently encounter in food, but it can remind us of the aroma of some inorganic substances in our daily lives. Try overdoing double-acting baking powder in a muffin, or making it with ammonium or potassium based leaveners instead of the widespread sodium ones, and you'll see what I mean. 

Beyond that, we don't really have good descriptors. And I am not even sure pretzels count - the goal there is to have the lye react away with the gluten, so they might not be very alkaline in the end. Also, the salt on the surface and the unusual texture distracts us a lot from the subtler flavors there.