I agree, I have to say that the "My Tournament" page is almost of no use whatsoever. If you're playing in half a dozen tournaments that have random meaningless names you need more info in front of you to determine what your position is within each one.
I have posted before the minimum useful info would be an indicator of which tournaments you have completed your round in, and a bonus would be a arrow up or down (or whatever pretty inhouse graphic) indicating if you've qualified to the next round or not. Eventually I would like to be able to archive/delete the list of tournaments, the same with the clan challenges.