If they have been known for a long time they may have been named for their discoverer (ie. Magellan for the LMC) or the constellation they are in (like Sagittarius). Today, they are usually named with just a number and a catalogue name. For example, the NGC catalogue which has hundreds of galaxies.
Karen was a graduate student at Cornell from 2000-2005. She went on to work as a researcher in galaxy redshift surveys at Harvard University, and is now on the Faculty at the University of Portsmouth back in her home country of the UK. Her research lately has focused on using the morphology of galaxies to give clues to their formation and evolution. She is the Project Scientist for the Galaxy Zoo project.