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?
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.
The actual pronunciation of the tetragrammaton is up for debate. If a person leaned toward "Yahweh" or "Yehovah," we wouldn't have a problem with that. But "Jehovah" is the most accepted version in English, and a viable translation.
Jesus is an acceptable English translation OF the greek version (Iesous) of a name that would more directly be transliterated Yeshua (which would be directly translated "Joshua"). Most of us recognize that and would have no problem with a more original pronunciation. But most of the biblical names translated into modern versions had a different original pronunciation... the point is that we recognize which individual is which.
No, we do not believe in a trinity and do not believe Jesus is a "person of a Godhead." But Jesus is still our lord and savior, the son of God, our messiah and king. We believe everything he said about himself, including what he said at John 14:28 and 17:3.
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.)
The question is answered well in the 2013 edition of the New World Translation appendix:
Much info on why Jehovah’s witnesses believe using the name Jehovah is important is found there. Specific to your question is the following:
Those who say that the divine name should not be used because it is not known exactly how to pronounce it will nevertheless freely use the name Jesus. However, Jesus’ first-century disciples said his name quite differently from the way most Christians do today. To Jewish Christians, the name Jesus was probably pronounced Ye·shuʹa‛. And the title “Christ” was Ma·shiʹach, or “Messiah.” Greek-speaking Christians called him I·e·sousʹ Khri·stosʹ, and Latin-speaking Christians Ieʹsus Chriʹstus. Under inspiration, the Greek translation of his name was recorded in the Bible, showing that first-century Christians followed the sensible course of using the form of the name common in their language. Similarly, the New World Bible Translation Committee feels that it is reasonable to use the form “Jehovah,” even though that rendering is not exactly the way the divine name would have been pronounced in ancient Hebrew.
Another great question comes to mind when looking at the picture below
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.
You used "Jehovah" when if to use it closer to Hebrew then it Would be Yahweh.
You say why don't JWs use the Hebrew for Jesus when you yourself use the English for God's name instead of the Hebrew yourself; why because that the natural way in our language.
We use the language common to the people in the land we live in. If I lived in Israel the I would use Hebrew, or in Greece I would use Greek but in England (USA) we the English version. Examples of Jesus' name in various languages:-
Isà عيسى (Islamic or classical arabic) / Yasū يسوع (Christian or latter Arabic)
Aramaic/Syriac ܝܫܘܥ (Isho)
Arberesh Isuthi Armenian Հիսուս (Eastern Armenian) Յիսուս (Western Armenian) (Hisus)
Belarusian Ісус (Isus) (Orthodox) / Езус (Yezus) (Catholic)
Bengali যীশু (Jeeshu/Zeeshu) (Christian) 'ঈসা ('Eesa) (General)
Catalan Jesús Chinese simplified Chinese: 耶稣; traditional Chinese: 耶穌; pinyin: Yēsū
Filipino Jesús (Christian and secular) / Hesús or Hesukristo (religious)
Georgian იესო (Ieso)
Greek Ιησούς (Iisús modern Greek pronunciation)
Haitian Creole Jezi
Hebrew Yeshua יֵשׁוּעַ
Hindustani ईसा / عيسى (īsā)
Hmong Daw Yexus
Indonesia Yesus (Christian) / Isa (Islamic)
Japanese イエス (Iesu)/イエズス (Iezusu)(Catholic)/ゼス(zesu) ゼズス(zezusu) (Kirishitan)イイスス(Iisusu)(Eastern Orthodox)
Kazakh Иса (Isa)
Khmer យេស៑ូវ (Yesu)
Korean 예수 (Yesu)
मराठी-Marathi येशू - Yeshu
Malagasy Jeso, Jesoa, Jesosy
Malayalam ഈശോ (Isho), യേശു (Yeshu)
Romanian Isus (almost all) / Iisus (Eastern Orthodox)
Russian Иисус (Iisus)
Serbian Isus / Исус
Sinhala ජේසුස් වහන්සේ - Jesus Wahanse
Scottish Gaelic Ìosa
Sylheti যীশু (Zishu) (Christian) 'ঈছা ('Eesa) (General)
Tajik Исо (Iso)
Tamil இயேசு - Yesu
Thai เยซู - "Yesu"
Ukrainian Ісус (Isus)
Vietnamese Giêsu, Dêsu