They will. This was most likely planned by their legal team in advance, will cost Facebook a negligible amount compared to their revenue and marked as a “risk.” And when they settle it will be a planned business expense, like a fine
Yeah they don’t even need to hire a law firm. They pay millions of dollars in retainer every year to keep lawyers on staff, so this is just someone’s day job to go through the motions
The company has said that they've spent a decade building their "brand" under that name. So, if they're pushing for a big payout, they intend it to be gargantuan rather than the usual payoff. Changing their name would essentially be starting over in some ways. And the confusion they claim as their reason for action is a legit thing.
I'm not saying that isn't their goal behind the scenes, but FB tried to buy the name and failed, so I have a feeling they aren't looking for the usual quiet payoff that's the goal of that type of action.