Two solutions come to my mind

An in-universe explanation would be, as Obi-Wan uses it, that Anakin "died" in a metaphorical sense when he became Darth Vader: he is no longer Anakin. Both Obi-Wan and the Emperor were wrong, as we can see in the end of Return of the Jedi: some of the "old" Anakin still remained in him, leading to his redemption.

An out-of-universe explanation would be just as simple as not to spoil the surprise at the end of the movie... "I am your Father".

Two solutions come to my mind

An in-universe explanation would be, as Obi-Wan uses it, that Anakin "died" in a metaphorical sense when he became Darth Vader: he is no longer Anakin. Both Obi-Wan and the Emperor were wrong, as we can see in the end of Return of the Jedi: some of the "old" Anakin still remained in him, leading to his redemption.

An out-of-universe explanation would be just as simple as not to spoil the surprise at the end of the movie...

"I am your Father".