Praise be to Allah.
Uttering the intention out loud when one is going to pray is bid`ah (an innovation), whether that is for Tarawih prayers or any other prayer.
Ibn al-Qayyim said in Zad al-Ma'ad (1/201):
When the Prophet (peace and blessings of Allah be upon him) stood up to pray, he would say: “Allahu akbar,” and he did not say anything before that, or utter the intention out loud at all. He did not say, “I am going to pray such-and-such a prayer, facing the qiblah, four rak'ahs, as an imam or following an imam.” And he did not say “ada-an (on time)” or “qada-an (making up a missed prayer)” or “fard al-waqt (the obligatory prayer of this time).”
These are all bid`ahs which were not narrated by any scholar with any isnad, be it sahih, da’if, musnad or mursal … Neither was this narrated from any of the Prophet’s Companions, and none of the Tabi’in or the four imams described it as mustahabb.
So the Muslim should have the intention of praying Tarawih in his heart only, and not utter anything out loud.
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And Allah knows best.