Logging is always good. So add logging.
I would prefer java.util.logging but feel free to use slf4j.
For the name: I know that there are evangelists that say that it must be upper case (because it is static final) but for me it doesn't matter. lower case is more readable in most cases (for the logger) and everybody knows that logger (or log) is for logging.
Also note that there is a class Log which is used for logging at some places.
Uwe