Why do certain airlines give names to their aircraft?
The practice of naming aircraft probably comes from the days of the flying boat, and the naval tradition of naming ships - the Pan Am Clippers had many named aircraft, and Pan Am kept up the tradition into the Jet Age. Other airlines of the period had similar naming practices (I'm not sure who started it, but Pan Am's fleet was well known for it).

As a marketing tool telling folks they're flying on "Clipper Emerald Isle from New York to Dublin" may have been more attractive to passengers than "Pan Am Flight 12345" or N880PA. Particularly before the commoditization of air travel, when flying was still a new and novel form of transportation, having a connection back to familiar "sailing" metaphors may have helped get passengers on board and could help differentiate your service from another airline. 

Modern airlines don't seem to push their aircraft naming as much as historic carriers did, but as SentryRaven noted there are a few airlines that still name their ships - in fact Lufthansa paints their plane names onto the fuselage, though I'm not sure if they announce them to passengers.
A skilled marketing department could build a brand around ship names, but I'm not aware of any airline doing so today.