Season 5 of Legends of Tomorrow changed Zari’s family name from Tomaz to Tarazi to show just how much things had changed because of Heyworld in the season 4 finale. That season ended with a massive change to the timeline, with Heyworld helping people to better understand magical beasts rather than fearing them — and one unforeseen consequence of this was the loss of a core Legend.
The season 4 finale saw Zari Tomaz disappear, replaced by her brother Behrad. Zari came from a future dystopian timeline in which her brother had been killed; him being replacing her in the present demonstrated that that particular future timeline no longer existed. When the Legends eventually met the version of Zari from the new timeline in season 5, she and Behrad were both using the last name Tarazi, a detail that Legends of Tomorrow showed but never elaborated on.
Zari’s name changed from Tomaz to Tarazi because the changes made to the timeline affected more than just magical creatures. In season 3, Zari Tomaz comes from a dystopian future where the Anti-Meta-human Act of 2021 eventually snowballed into ARGUS instituting a police state across the United States. Beyond the persecution of meta-humans, this also led to a crackdown on religious freedom, which according to Legends of Tomorrow writer Tyron B. Carter, led to the family changing their name from Tarazi to Tomaz to hide their background (via Twitter).
In season 5, the Zari of the new timeline didn’t grow up in that world. Zari Tarazi lived a much better life as child celebrity turned entrepreneur, Behrad wasn’t killed by ARGUS, and her family never had to hide their heritage, keeping their original name. While the name change isn’t called out too explicitly by the show, Zari’s change in personality is, being a bubbly social media mogul rather than a cynical hacker from a ruined future. The new future also completely changed Zari’s relationship with the Legends: In the new timeline, Behrad was a member of the Legends, though Zari discovers that he’s up to something when she sees him and Nate in footage from Heyworld in 2019 looking exactly the same as their appearance in 2044. She eventually joins the team, but through far different circumstances than the original timeline.
Changing her name also helps distance Zari further from her DC comics inspiration. Her original name, Zari Adrianna Tomaz, is an obvious reference to the character Adrianna Tomaz, and the air totem is based on the amulet Tomaz gets her powers from. Legends hasn’t drawn too many connections to Zari’s comics counterpart because, according to Marc Guggenheim, they “didn’t want the baggage” of using her comics name, Isis, when the terrorist organization ISIS exists, especially considering Zari’s Muslim background (via Entertainment Weekly). Adrianna Tomaz is also reported to be in the Black Adam movie, so this helps make Zari a more distinct character from the movie’s version.
While she was originally Zari Tomaz, Zari’s family name has changed to Tarazi in season 5 of Legends of Tomorrow. In-universe, this is because the Legends changed the timeline at the end of season 4, while also serving to distance her from her comics counterpart.