Instead of naming my invoking class, I started using the following:
private static readonly ILog log = LogManager.GetLogger(System.Reflection.MethodBase.GetCurrentMethod().DeclaringType);
In this way, I can use the same line of code in every class that uses log4net without having to remember to change code when I copy and paste. Alternatively, i could create a logging class, and have every other class inherit from my logging class.