was wondering if ‘Khuda’ used as a name for Allah(swt) considering it has its origin in Persian/Zoroastrian culture.

Also, has the word – Khuda – ever been used by our Holy Imams(as)?

Imams are Arabs and so they always used Arabic language. Khuda is used as translation of Allah in both Persian and Urdu languages. And there is nothing wrong with that.
Yes, it may not give the whole meaning of the word “Allah”, but it’s the closest