This could end up like the case where someone called Mike Rowe was sued by Microsoft for starting a company called MikeRoweSoft. He settled that case and changed his name but got a pretty decent deal outta it. Also, it was felt in that case that he could have won the case had it gone all the way cos it was a legitimate use of his name (not like Liberty X, as I doubt any of them are actually called Liberty), and as Mika is actually called Mica, whereas little miss lawyer friendly is called Sophie, he sure has that going for him. Plus, since her career is hardly a success story, any damages she could be awarded would me minimal, unless she's awarded punitive damages, which is illegal so damn unlikely. And, as she's demanding what are no doubt excessive damages anyway (would have to see how much she's demanding compared to how much she's actually lost as a result of Mika using the name) Mika could just say it's a claim made in bad faith, as she's just hoping to make a quick profit out of the case. Anyway, if anything I'd say she's probably profited from it anyway, cos some muppets are bound to have accidentally downloaded her song mistaking it for our Mika.
Anyway... sorry to go all lawyer on you guys... just my opinion.