If the hacker's use of his most common alias' first name is meant to alarm him, she has underestimated Finch as severely as he'd underestimated her when he'd first begun backtracking the Trojan virus from Scott Powell's computer. There are any number of ways she could have obtained it; he has not precisely been sparing of its use in recent months, and he is of course excruciatingly aware of the vast array of surveillance data constantly collected in the city and the multiplicity of ways an unscrupulous person might tap into it.
He is intrigued, however. Had she already known that name when she'd created the false data to set up a patsy for the congressman's shooting? Had she been anticipating the likelihood that Finch and Reese would intervene? Or had she researched them after they began skewing her carefully engineered plan off course?
Either way, there must be other connections somewhere in the Venn intersection between her sphere of influence and theirs. Her conviction that there will be a "next time" virtually ensures it. Uncovering those connections is likely to be quite an involved process.
Reese has teased before that there is no Machine; there is only Finch himself. That is not, literally, true. What is true is that someone had had to teach the Machine what to do, and what better teacher than the man who had designed it? Finch sees patterns everywhere he looks, and speaks the language of digital warfare like a native; complex intellectual problems are his bread and butter. Root has misstepped by throwing down this gauntlet.
That is a common failing in those who succumb to the lure of power, he has found: an urge to prove themselves against the strength of others. Particularly in the young; and she can't be more than Will's age, at most, to have blended in at that dorm. Fortunately, neither is an ailment from which Finch suffers. And he has resources that she will never be able to match-- in quality, if not in nature.
That thought reminds him of his partner, and he surreptitiously pulls up the tracking data for Reese's new phone... and for Zoe Morgan's. They had stood in proximity outside the Powell residence for some considerable length of time; and though they'd departed separately, Finch would not be surprised to see their indicators in close company again at some much later hour. There had been appreciation in her eyes when she spoke of his partner; and from his swift reaction to the simple mention of "she" in context with political maneuvering, Ms. Morgan seems to have left an impact on Mr. Reese as well.
Good. It might prove beneficial to have Reese's sharp attention diverted while Finch takes his next few steps. He has not missed the fact that Detective Fusco has been pursuing "another assignment" of late.
He packs up his laptop, then calls for a driver and limousine.
As Will might say, if Finch trusted him with the truth: Game On.