I think everyone knows that the name Jesus is Greek, but why don’t Jehovah’s Witnesses use his Hebrew name, which is closer to Joshua than to Jesus?
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There's a problem with one of your assumptions: Jehovah's Witnesses don't use Jehovah "to be accurate". They use Jehovah because they think it's important to call God by name, and because Jehovah is the traditional rendering in English. They accept that the original pronunciation has been lost, and argue that were it important, Jehovah God would not have allowed it to be lost. They do make linguistic arguments in favour of a trisyllabic pronunciation, but these are lesser considerations.
They also remark that many names contain elements of the divine name: Jeremiah and Jehoshaphat, for example. They argue that if you were to change Jehovah to Yahweh, you should, for the sake of consistency, change these names too.
For more information, see their official publication The Divine Name that Will Endure Forever.
This is my understanding from studying with a JW who visited my home and became a weekly visitor over the course of several months. (I am not JW, but am not opposed to study.) During the course of this study, I was informed that they (JW) do not believe in the trinity. They are not concerned with honoring Jesus in the same way that God should be honored.
(Also, the correct name for Jesus, according to Jewish tradition is Yeshua.)
Its the same reason why Jehovah's Witnesses use Jehovah which is not Hebrew or Greek.
What matter most is that you are using the accepted equivalent translation in your own language or dialect to pertain to God or to his son, Jesus, and you are not constraint of using their names because of their original pronunciation is lost through time.