This is difficult to translate, mainly because modern Vietnamese uses a phonetic writing system based on the Latin alphabet.
I suggest you go back and look through your ancestors’ genealogical records.
Otherwise, if “Cao” is translated as “曹” or “操,” it could be embarrassing.
If you can find your great-grandfather’s tombstone, you should be able to see which “Chinese character” your surname actually corresponds to in the inscription.
The inscription on the stone has been preserved for over 1,000 years.