Stannis Baratheon gave us a pretty good summary of how the history books remember Rhaenyra Targaryen. While it's easy to sympathize with the character as The Rightful Queen due to her depiction in House of the Dragon, the in-universe books and the novels the shows are based on say otherwise. The first season didn't really show audiences much of the reason for Rhaenyra's well-deserved nickname (more on this later on) but Season 2 won't shy away from this.

Queen Rhaenyra Targaryen will go from "The Realm's Delight" to "Rhaenyra The Cruel" and "King Maegor with teats" over the course of the next few seasons of House of the Dragon.
And, a set video from the in-production Season 2 of House of the Dragon will show why.
A set of photos and videos show a bloody cart parading a huge blue dragon head prop around King's Landing, as someone shouts "Behold! The traitor dragon Meleys - slain at Rook's Rest for your king! for Aegon!"
Meanwhile, in a separate video, the Greens are attempting to persuade the public by showing a funeral procession with a crier telling everyone to look at what "Rhaenyra the Cruel" has done.
It's a macabre moment that proves that history will be written by the winners, which, at this point in time, was the Greens.
With her husband/uncle, Daemon Targaryen, at his side pushing him into open war/rebellion against the crown, Rhaenyra will likely have to do unsavory things to earn her nickname. But, it's highly unlikely that she'll go far enough to warrant a comparison with Maegor the Cruel.
After losing two of her children at the tail end of Season 1, Rhaenyra has every bit of a reason to feel vengeful against the Blacks.
Whether or not we'll learn more about her actions in the show than what was told in the books is something that we'll have to wait for a while to find out.
Although, at the end of the day, both Rhaenyra and Aegon II aren't seen in the best light in the history books. The former is treated as a usurper, even by her descendant, Stannis Baratheon. On the other hand, Aegon II is usually deemed by the history books as an incompetent king who was unfit to rule. Both will walk out of the Dance of the Dragons with their lives forfeit and reputations tarnished forever. But, at least we'll find out the "truth" behind the events of the Targaryen Civil War.
House of the Dragon Season 2 is currently under production. While the ongoing writer's strike isn't expected to affect the filming process, reshoots and post-production are a different story. If the current situation doesn't improve, House of the Dragon Season 2 might miss its current release window.
House of the Dragon 2 will have fewer episodes compared to Season 1. Season 3 is likely already confirmed but we're still waiting for official news.