I don't think I ever heard any Borg call her Queen, or any numerical designation. I don't even remember 7 of 9 call the Queen by any designation. Would she be 1 of 1? 1 of 1 because there is only one Queen at one time.
All of Everything. It woud depend on how many Queens there were, I've considered that there might be several, each running a section of the collective.
TrekLit notwithstanding, I'd go with "The Assimilation Anomaly", or if you wanted something cool to dig into later, "Assimilation Anomaly #2".
She gave her name on screen. She literally self-identifies as "the Borg." As in, "I am the Borg." Her name is the name of an entire species.
One Borg to rule them all, One Borg to find them, One Borg to bring them all and in the darkness bind them
Or rather, the Borg is the entire species, and the Queen is merely its central coordinating node. When she speaks, it's the entire collective mind that's speaking, simply focused through that particular body. Which is why the Queen can't be killed. Destroy the Queen, and the Collective is incapacitated for a bit, but it simply plugs in a new Queen component and restores full function.
I always thought of her as the personification of the Borg Collective. I just thought she might have a designation other than "I am the Borg". Though the biblical connotations of "I AM" just hit me now.
But what is a "personification" except the thing that gives the whole a face and a voice? "Person" comes from the Latin word for an actor's mask. The Borg Collective is a single mind that is formed from the collective activity of trillions of separate drones, but since the "Queen" coordinates all those separate threads of mental activity and focuses them through a single body, a single face and voice, that creates for us the perception that the Queen embodies/personifies the Borg. Heck, that's the literal reason the character of the Queen was created in the first place -- to make the Borg a more personified threat, to make them a character rather than just a faceless force of nature.
They were more threatening as a faceless force of nature. Before TrekLit took up the issue and provided an alternate explanation that I am willing to accept, begrudgingly, in the Destiny books, my personal preferred explanation was that she was someone the Borg tried to assimilate from a species with either powerful mental gifts or advanced cybernetics, and she kind of assimilated them, instead. Which is what I meant earlier in the thread by referring to her as "Assimilation Anomaly".
I agree. But they're also harder to tell stories about that way. Stories are about people, after all, so a totally depersonalized threat isn't very conducive to drama. That's why TNG retconned the Borg from being totally uninterested in living beings in "Q Who" (remember, the drones there were incubated from embryos) to suddenly giving a damn about humanoid authority structures and assimilating Captain Picard in "The Best of Both Worlds." It was necessary to give them a voice and a more personal focus in order to tell more stories about them. And thus we also got Hugh and Seven of Nine and the Borg Queen. It's not the first time or the last that an impersonal alien menace in SFTV was given a more personalized individual who could function as a character rather than an unfocused threat. Doctor Who did it when they introduced Davros, the creator of the Daleks. Dalek stories had grown rather stale and repetitive by that point -- Terry Nation was basically plagiarizing his own earlier stories without realizing it -- and once this was pointed out to him, he worked with the producers to add something fresh to the concept, and thus Davros was born in "Genesis of the Daleks," and was featured in every subsequent Dalek story until the end of the original series. And later, Stargate SG-1 had the Replicators, which were just insectlike self-replicating robots for several seasons but then "evolved" into androids so they could talk and have personalities and participate in stories as characters. Eventually you run out of stories to tell about taking on a faceless threat, because there are only so many ways to tell it. Giving it a face and a voice allows writers to use more of the tools in their kits.