You can extend the Spring class HandlerInterceptorAdapter to create a new interceptor which will be invoked before the Controller is invoked.
In it's preHandle(HttpServletRequest, HttpServletResponse, Object handler)
method, the handler is the controller wich will serve the request, and therefore you can log the controller's name in your log files. Remember to set the log level accordingly for this class.
You need to add this interceptor to <mvc:interceptors>
in your spring-mvc-config.xml.