Coming from someone who doesn't have a legal background at all here, but doesn't the fact that he quit the band automatically make his argument about the name to be worthless?
There will have been various legal agreements that Portnoy was involved in as part of the band that will have had to be disentangled before he was technically no longer part of the band.
I think from past interviews they've given that essentially the five members of the band are the significant shareholders in the Dream Theater rights and pay out dividends to themselves at the end of the year and the rest of the time they pay themselves a pittance. I think this is the way it works and it means they can get a lower rate of tax than if they were just paying themselves a set wage (someone with better understanding/knowledge of US business will know more than I).
Admittedly this is all speculation, but when it comes down to the brass tacks of extricating Portnoy from the business dealings there will be a certain claim he can attach to future earnings based on having helped build up the Dream Theater brand for so many years.
I suspect if he were touring with A7X right now and making decent money that the lawsuit might not have happened, but since he's now looking at a big hole in his earnings he's going to use the courts to arbitrate how significant his involvement was up to this point and try and get himself a bigger slice of the future pie than DT are willing to hand over.
I don't think it's actually that rare a thing to do and there are more absurd lawsuits that have been floating around (e.g. David Ellefson vs. Dave Mustaine, suing him for $17M wasn't it?). I believe from what was said of the Alex Lifeson court case a few years ago that lawyers will advise their clients to sling as much against the wall as they can to see what sticks.