Get Route Event Layer Source Table Name

I have a Desktop Add-In built with C# that provides additional UI for working with some route event data. I want to ensure the user interaction between the map layers and the underlying data table stays connected, even if the layer name gets changed. I also want to guaranty that the correct event layer is in the map.

So the question is, given a Route Event Layer, how do I use ArcObjects to access the underlying table? Specifically, how do I get its name in the database?