Vernor Vinge seems to point in a few possible directions for clues on the identity of Rabbit. The strongest is the one first suggested, that Rabbit is an AI program. Keiko Mitsuri and Günberk Braun seem to think so, mentioning that the crossover point for hardware and networks had been reached to allow such an AI, along with their statements as to its juvenile personality. The strongest evidence for this view is the very fact that Alfred Vaz ridicules the idea, given that he is in the process of deceiving these same intelligence colleagues.
Vaz seems to know what Rabbit is. For one, Rabbit notes that he had left behind so many clues (including the carrot greens) as to his identity, and Vaz confirms this in Chapter 32, when he is convinced that Rabbit was the Next Very Bad Thing due, in part, to the carrot greens left in his office network in Mumbai.
However, Vaz does mention that the minds behind Rabbit had been reduced to ignorance after the revocation attack, and it is not clear that these minds are Rabbit's creators or Rabbit itself. As to the identity/ies of these minds, there are some intriguing possibilities.
Rabbit may be DHS. This is a weak argument, but in Chapter 33, Bob Gu, Jr. is "minded" by DHS agent Eve Mallory. At one point, she says "Heh. We'll figure it out. A network attack on a bio-prepped victim - that's a technology that's way to interesting to ignore." Besides the tell-tale "Heh" which I associate with Rabbit, the rest of the statement just sounds like Rabbit.
Rabbit is some kind of ego-level AI program. I had a sharp sense of deja vu when comparing the following statements:
"For Robert Gu, real creativity most often came after a good night's sleep, just as he roused himself to wakefulness. That moment was such a reliable source of inspiration... There in the labile freshness of new consciousness, answers would drift into view."
"Rabbit was not always fast. For hard problems, he was like lesser beings; he had to sleep on the question. Then in the morning, the old intuition would deliver remarkable insights."
"Over the past twelve weeks, Rabbit had learned a lot; he had grown, you might say."
Could Rabbit have been "born" or at least instantiated when Robert regains his self-awareness (or as Robert said, his "marbles")? Maybe this happened at UCSF when he went in for the Alzheimer's cure. There is precedent for this view in Vinge's other novels. I think of Arne and Sjana as transcendent ego-level programs based on Jefri and Johanna's actual parents in A Fire Upon the Deep.