In English, the word; "Carrow", can refer to two places. "Carrow" in Norfolk, or "Carraw" in Northumberland. The first is assumed to have its name derived from the Old English word "carr", meaning "rock", and a word of Celtic origin; "hoh", meaning "spur of a hill". While the second appears to have been named either after the plural of the Old English word "carr", or after a mixture of a form of "carr", and another Old English word; "raw", meaning "row".
It is also possible that the surname was originally a shortened version of the Cornish surname; "Nancarrow".