Who gives a newly discovered microbe its name?
I sthere any reason for your question to be specific to microbes? Whether a microbe or multi-cellular organism is found, the problem is the same. Who name it?


  Who name it?


Whoever discovered it. Of course, discovering a new species is not as easy as just taking a picture. One has to provide a very thorough description of the species morphology and eventually argue that it should be considered as a new species and not just as a subspecies or something else. See here for discussion on the definition of a species.


  How does the discoverer name it?


If the new species is considered part of an already existing genus, then the author has to keep the genus name. The species name the author chooses is mainly to up himself / herself. Consider for example Macrocarpaea dies-viridis (dies-viridis means "green day") was named like this because the researchers were listening to Greenday when they found it!