Joule-hour is Watts * 3600?
In other words, let's say I have a 100 Watt light bulb and it runs for
  3 hours. Then energy consumption would be 100 * 3600 * 3 = 1,080,000
  Joule-hours. Is that right?


No, there is no need to say anything other than joules.

Your lightbulb has consumed, over the 3 hour period, 1,080,000 joules of energy. It's as simple as that.

If you had a tap running to fill up a 1000 gallon container and it took one hour to fill the 1000 gallon container you wouldn't say you have used 1000 gallon-hours of water. That would be stupid.