We learn in The Empire Strikes Back that Kenobi had lied to Luke in A New Hope about Darth Vader, telling him Vader killed his father rather than the truth that Vader is actually his father.
Why the lie?
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The real answer is more mundane than you think. It's simply because at the time of writing Star Wars, the writers did not yet have Vader being Anakin Skywalker, Luke's Father. That was not decided until the second draft of Empire Strikes Back. The same thing happens to the Luke/Leia being siblings, and likely the Obi-Wan and Anakin being master and apprentice.
You can't lie about what you don't know yet.
Of course, if we considered in-Universe Canon, retroactive continuity, the answer is psychological. Ben considered Anakin, the person he knew, as figuratively dead, when Anakin made a complete 180 in personality and his evil actions (gave in to the Dark Side). Vader was not the man he knew anymore. A bit more in depth, Ben considered himself dead too. Obi-Wan died when Anakin forced Obi-Wan to kill Anakin, figuratively speaking. Hence dropping the Jedi name. There's also a bit where Ben might not 100% know Anakin survived.