Projects needs names. Bear is just a name for this project. There is no deep message encoded in the name... I like to choose names which are not specific to the job the tool (or service) is doing, because the function might change overtime. So, picking a name like "Jenkins" for a continues integration service is great (instead of calling "continuous integration service").

With bear, I was playing with words. It can be interpreted just a name as "bear", but if people want to connect it to the functionality it can be "build ear" because it listens to your build (and generates compilation database as output).