Star Trek: Deep Space Nine's U.S.S. Defiant originally had a different name — the "tough little ship" was meant to be called the U.S.S. Valiant — but the starship's designation had to be changed because of Star Trek: Voyager. Debuting in 1992, DS9 was the first spinoff of Star Trek: The Next Generation and, because it was set on a space station, it had a unique premise for a Star Trek series — but one that alienated Trekkers who insist that a Star Trek show needs to be set on a starship.
Although Star Trek: Deep Space Nine wasn't entirely without vehicles since the station used three Runabouts, which were warp-capable, shuttle-like vessels, but the meager Runabouts were a far cry from an actual starship, and it hindered the ability of DS9 to tell stories that could explore the adjacent Gamma Quadrant. By DS9 season 2, the writers had introduced the series' Big Bads, the Dominion, which ruled the Gamma Quadrant and consisted of three core races: the shapeshifting rulers called the Founders, their violent legions called Jem'Hadar, and their mouthpieces called the Vorta. It quickly became clear to DS9's showrunner Ira Steven Behr that the station's Runabouts were insufficient to fight the series' great menace. Further, as executive producer Robert Hewitt Wolfe pointed out, "the Runabout sets sucked" because they were cramped to shoot in and entire episodes couldn't be staged aboard a Runabout as opposed to a real starship.
Deep Space Nine desperately needed a starship to realistically fight the Dominion, but Paramount resisted the idea because the studio felt that DS9 having their own ship would clash with Star Trek: Voyager, which launched in 1995 and was styled as the new flagship Star Trek series and the successor to Star Trek: The Next Generation. Still, Behr and DS9's writers ultimately won their quest to get their show a starship, even though Star Trek executive producer Rick Berman, who wasn't fond of the idea, insisted it "had to be [a] small [ship]", i.e. smaller than both Voyager and TNG's U.S.S. Enterprise-E. DS9's solution was the starship that would become the U.S.S. Defiant, a tiny but heavily-gunned warcraft. But it wasn't called the Defiant at first; rather, the ship was named the U.S.S. Valiant — a name Paramount shot down.
The studio issued an edict that DS9's new starship couldn't be called the Valiant because the name starts with the letter V, which is "too similar" to Star Trek: Voyager's titular vessel. So instead, executive producer Ronald D. Moore pitched the name "Defiant," which is what they went with (and spiritually links DS9's warship to the identically named Constitution-class starship from Star Trek: The Original Series' era). Paramount's demand for the name change spoke to the franchise's internal politics and how much the studio valued Star Trek: Voyager as the purported flagbearer of the franchise, as opposed to DS9, which was considered Star Trek's "middle child" and a black sheep.
Regardless, DS9's U.S.S. Defiant was immediately popular with fans, and it even made its big-screen debut in 1996's Star Trek: First Contact. The Defiant opened up vast storytelling possibilities for DS9 and it gave Captain Benjamin Sisko (Avery Brooks) the necessary firepower to fight the Dominion War, which dominated the final seasons of the series. The mighty Defiant was ultimately destroyed in DS9 season 7, but Sisko soon received an identical starship, the U.S.S. Sao Paulo, which was then rechristened to become the new U.S.S. Defiant.
Ironically, DS9 season 6 introduced a Defiant-class starship called the U.S.S. Valiant anyway. In one of the darkest episodes of the series, the Valiant was behind enemy lines and piloted by an elite group of Starfleet Cadets called Red Squad. After rescuing Nog (Aron Eisenberg) and Jake Sisko (Cirroc Lofton), the fanatical Red Squad underwent a suicide mission against the Jem'Hadar that got almost everyone aboard the ship killed. Despite the grim nature of the episode that led to the destruction of the U.S.S. Valiant, the ingenious Star Trek: Deep Space Nine still got the last laugh over Paramount.