"More accurately bismillah means 'in the name of Allah'"
If you choose to not fully translate the Arabic phrase... but then it becomes less accurate, somewhat on a par with 'bismi God'.
'Allah' is an Arabic term for 'God' that predates the Islamic use as the true name of God. Arabic speakers of all Abrahamic faiths, including Christians and Jews, use the word 'Allah' to mean 'God'. 'Allah' also appears in Sikh scriptures, Hindi and Punjabi amongst many other eastern languages.
'Bismillah' is a ritual invocation spanning a number of eastern religions including Zoroastrianism, the religion in which Farrokh Bulsara (a Parsi) was raised.