What is the place Jews worship God in their houses called?

1) Synagogues. Public prayer services are part of halakha (Jewish law) and tradition (Talmud, Berakhot 26a).
Prayer is an important form of communicating with God, and maintaining a relationship with Him; and it is also good for the health of the soul, to which Torah, prayer and religious observances are a form of nourishment.

2) The Temple, which stood in Jerusalem and was destroyed by the Romans 1945 years ago.