I think that the relevant naming 'authority' for e.g. craters on the Moon (and Mars) is the International Astronomical Union. Besides weak spots in the system, the basic idea is that people or institutions can propose names for a crater. This is usually done for paying respect and honour to important and/or deceased members of the space exploration and astronomy communities. Notable examples are the Tsiolkovskiy crater (after Konstantin Tsiolkovsky) or a group of seven lunar craters named after the crew of STS-51-L.
I have observed that the teams of e.g. the Mars Exploration Rovers and Mars Science Lab also give names to a lot of objects, rocks and mountains etc along their routes. Those names are then used in (scientific) literature, too. What are the official procedures for naming such objects, if there are any? Do they accept proposals (from non-team-members) and/or are there examples of this happening in the past?
As odd as this question may be, it is relevant with respect to 'exploration'. The first thing humans do, if they discover something new, is giving names.