The last champion name stays there till the new champion's name replaces it. Basically, it always 'honors' someone.
What you need to see in order to know that the tournament has started is this above the current champion's name:
"The ongoing tournament finishes at:
on nn/nn/nn at nn:nn time"
And then on the right side of that it should say:
"Time remaining:
n d"
Where n is a random number and d means days. Also, when a tournament hasn't started, the wording of the first would say when the last tournament has ended and there would be nothing on the right side.
Hope that helps!
ETA: Oh, and no, doesn't mean you should have earned any points by now, was just stating that I had already earned that many in Iron Age by that time. 18k now.