Disillusioned JW : The expression of "by divine providence" is the wording of the WT's NWT.
That will teach me to compare translations before quoting what I am familiar with. I did find that Young's Literal Translation (1898) reads similarly to the NWT - "the disciples also were divinely called first in Antioch Christians" - but certainly most translations make no reference to divinity in that passage.
I wondered why the NWT read differently and found a Question from Readers which discussed it. There it says :
The translation so reads because that is what the original Greek word seems to mean. The verb chrematízo in question occurs nine times and the noun chrematismós occurs once, and by referring to these occurrences and noting how the translation reads in each one, you will appreciate that these Greek words are always used in connection with what is from God and hence divine in that sense. See Matthew 2:12, 22; Luke 2:26; Acts 10:22; 11:26; Romans 7:3; Hebrews 8:5; 11:7; 12:25, and Romans 11:4.
In Vincent's Word Studies it says that chrematísai originally meant to transact business, to have dealings with; thence, in the course of business, to give audience to, to answer, from which comes its use to denote the responses of an oracle; a divine advice or warning. See Acts 10:22; and compare Matthew 2:12; Hebrews 11:7. Later, it acquires the meaning to bear a name; to be called, with the implication of a name used in the ordinary transactions and intercourse of men; the name under which one passes.