The new Rorschach's name is Reggie, revealed in Doomsday Clock #2, and it would not be a stretch to say that the scene in which this information is revealed probably gave a lot of fans the inkling that their theories hold water.
In Doomsday Clock #1, Rorschach took off his glove to reveal that he was a black man. It was a gesture of goodwill extended to The Mime in order to prove to her that he was not the man who put her and her husband behind bars. There was no explanation of his backstory, though, and so fans of course did what they do best: They speculated.
The most popular theory is that the new Rorschach could be the son of Malcolm Long, the psychiatrist at Sing Sing who treated Walter Kovacs -- the original Rorschach -- while he was in jail.
While Long did not specifically say that he was a father in Watchmen, Long was one of only three significant black, male characters and so fans were tempted to associate him with Rorschach right away. One panel from Watchmen depicts a coffee mug on Long's desk that says "Dad," which was enough evidence for many fans to jump on the notion that this Rorschach -- who stammered "it's good to have family" in the first issue of the miniseries -- could be Long's son.
So, why would the name "Reggie" make that more likely?
It doesn't. What makes it more likely, at least arguably, is the scene in which the name Reggie is first uttered by Ozymandias, who is trying to calm Rorschach down.
After arriving in the DC Universe via Nite-Owl's ship, Rorschach is briefly unconscious. When Ozymandias attempts to revive him, Rorschach's first instinct is to leap at Ozymandias, threatening to kill him, before Veidt reminds Reggie that the two have an agreement to save the world.
That fury at Veidt might be easy to understand if, for instance, Rorschach's father was killed during the "alien invader" attack on New York, which Long appeared to be.
Is this a hint? A misdirect? Or will it build to something else entirely? Hard to say just yet.