It would be a massive understatement to simply say that The Legend of Zelda: Breath of the Wild was a hit. The game completely changed how many people defined the series and its traditional mechanics. By taking the franchise back to its adventure/exploration roots, Nintendo was able to reignite the passion and excitement many of its fans had for the games. As the development of the Zelda: Breath of the Wild's sequel continues to be, mostly, radio silence, plenty of fans have been speculating about what's in store for Breath of the Wild 2.
Despite many using "Breath of the Wild 2" as shorthand for the name of Breath of the Wild's untitled sequel, Nintendo hasn't said anything about the game's official name. In fact, looking at the series' history could likely debunk this name outright.
Legend of Zelda: Breath of the Numbers
Mainline entries in the Legend of Zelda series very rarely get direct sequels. The last to do so was Phantom Hourglass with its sequel Spirit Tracks on the DS back in 2009 and before that was Ocarina of Time's follow-up Majora's Mask back on the Nintendo 64 in 2000. In fact, the only Zelda game with a numeral in its title is Zelda 2: The Adventure of Link.
Even with The Adventure of Link, the official title for the game drops the "The Legend of" so the game isn't even called "The Legend of Zelda 2." All of that is to say it seems unlikely that Breath of the Wild's sequel would simply be called "Breath of the Wild 2." So far, in the handful of times that Nintendo has officially addressed the game, it's been called variations on "the sequel to The Legend of Zelda: Breath of the Wild."
Before February's full-length Nintendo Direct, there was speculation based on a faked leak that the sequel would be revealed under the title The Legend of Zelda: Echoes of the Past. While the reveal didn't happen during the Direct (along with a laundry list of other "too-good-to-be-true" leaks), the use of "Echoes of the Past" in place of "Breath of the Wild 2" has gained some minor popularity among the Zelda community. It's unlikely, however, that the game's official name is The Legend of Zelda: Echoes of the Past as the leaked list of Nintendo Direct highlights was almost entirely fictional.
Capturing the Spirit and Maybe the Title
It's worth noting that, as stated above, Nintendo has only ever called the game variations on "the sequel to Breath of the Wild" and never "Breath of the Wild 2." While it seems unlikely that the game would get a numerical sequel title, Nintendo revealed that Breath of the Wild was meant to capture the spirit of adventure and exploration in the original Legend of Zelda. Because Nintendo was trying to reinvent the series by exploring the concepts that made the original game so appealing, the company might also follow the original game's lead by giving the sequel a simple, numerical title with "Breath of the Wild 2."
All of this speculation eventually concludes by pointing out that, currently, there is no official answer. Whether it's "Breath of the Wild 2" or "Echoes of the Past" or something else entirely, it's not looking like anyone outside of Nintendo will know until the game's official title reveal, hopefully at E3 2021. If not then, Nintendo should still be providing news on the game's development later this year as producer of the Zelda series Eiji Aonuma promised in February's Nintendo Direct.
The Legend of Zelda: Breath of the Wild is currently available on the Nintendo Switch and Wii U.