While many Magic: The Gathering set names have gone through name changes, only Urza's Saga had one nixed then (technically) used later for an odd reason.
One of the most underrated parts of Magic is the set or expansion name. With only a word or handful of words, you need something unique, ear catching, and something that tells you a bit of what it is about before you even see or play it. Tarkir: Dragonstorm? Well it takes place on Tarkir and there be more dragons than usual. Aetherdrift? Well that energy is there and drift refers to drift racing. Bloomburrow? Flowers and homes for animals. It's both a hint and doesn't give away too much.
And Magic has a whole history of thought up and rejected names. Most we don't know, as R&D thought them up and rejected them, never to be seen by the light of day. A few made it into planning or design until the names were changed. And still others were rejected the first time around, but then green-lit for the sequel. In fact, there is a whole process in getting name approvals, with it needing approval by creative, other Magic higher-ups, and then Legal.
For these we know of a few. Mirage was originally called Menagerie. Streets of New Capenna was Streets of New Celestia during design. Khans of Tarkir? It was Warlords of Khanar. Throne of Eldraine was Throne of Ardenvale. For the Tarkir, creative loved and approved the name, but the legal department said no. As for Throne of Eldraine, it was simply because someone didn't like the name Ardenvale, although the team kind of got back on them for this one by naming a castle Ardenvale and having it be released as a card.
And then there is the story of Urza's Saga. Released in 1998 as the first expansion in the Urza block, Urza's Saga began life as Urza's Odyssey. In fact, development under this name made it pretty far. But, like with Khans of Tarkir, legal said no.
But then the fun part. A few years later a new expansion was named Odyssey and it went through. Confused developers went to the higher ups and the simple answer was...different lawyers. Multiple Magic sets were named, renamed and then had names kept simply because of a change of legal teams.
While name changes still undoubtedly happen today, a change of legal teams is most likely not the reason why other sets can have the name.