If you are utilizing web client, the agents should be built using a web client rather than classic. The web client offers a really easy way to copy agent profiles to a new agent profile so that you don't have to create an entire new agent.
The preferred way of building agents is to build them new, not change people's names on the agent profile. I have seen it cause problems before with reports with this very same symptom, being able to run reports by agent ID but not by name.