Java Custom Logger - Not logging proper classname

I am trying to create a Custom Logger. My code is given below and the Properties file is also given below.

It works in the sense that I get log messages and details in the log file in the format I want. However, all logs are logged with same ClassName - MyLogger. I want the 'name' I am passing in the constructor to be logged as ClassName instead of the MyLogger ClassName. Appreciate any help in that regard.

Java Code:

    public class MyLogger {

    private static Logger log;
    
    public static MyLogger getLogger(String name) {
        return new MyLogger(name);
    }

    private MyLogger(String name) {
        log = Logger.getLogger(name);
        try {
            LogManager.getLogManager().readConfiguration(new FileInputStream("./logging.properties"));
        } catch (FileNotFoundException ex) {
            Logger.getLogger(MyLogger.class.getName()).log(Level.SEVERE, null, ex);
        } catch (IOException | SecurityException ex) {
            Logger.getLogger(MyLogger.class.getName()).log(Level.SEVERE, null, ex);
        }
    }

    public void log(Level LogLevel, String logMessage, Object param1) {
        log.log(LogLevel, logMessage, param1);
    }

    public void log(Level LogLevel, String logMessage, Throwable e) {
        log.log(LogLevel, logMessage, e);
    }

    public void log(Level LogLevel, String logMessage) {
        log.log(LogLevel, logMessage);
    }
}

logging.properties File content:

handlers = java.util.logging.FileHandler
java.util.logging.FileHandler.level     = ALL
java.util.logging.FileHandler.formatter = java.util.logging.SimpleFormatter
java.util.logging.SimpleFormatter.format = %1$tF %1$tT %4$s %2$s %5$s%6$s%n
java.util.logging.FileHandler.limit     = 1048576
java.util.logging.FileHandler.count     = 5
java.util.logging.FileHandler.append    = true
java.util.logging.FileHandler.pattern   = ./logs/log-%u-%g.log

--

The documentation for SimpleFormatter.format explains that the source parameter (%2$s in the format string) is "a string representing the caller, if available; otherwise, the logger's name". This looks at the stack to determine the direct caller, which in your case will always be the MyLogger class.

To use the logger name instead, use %3$s in the java.util.logging.SimpleFormatter.format configuration rather than %2$s.