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Carrow is a common name in Southwest England, particularly in Cornwall. There is an old ditty about Cornish names that goes:
"By Tre-,Ros-,Car-,Pol, and Pen ye shall know the Cornishmen." The Celtic name prefixes cited above are references to place names as opposed to persons or occupations which is more common in English surnames. The prefix "Tre" refers to a town or enclosure; "Car" refers to a fortification or camp, particularly made of stones; "Pol" refers to to a pool, "Ros" indicates a heath or moor location; and "Pen" refers to a headland by the sea. Thus a name like Carrow refers to a fortified or built up place made of stone in a row, or most likely, a wall.
Carrow has been spelled many different ways over the ages including Carro, Carrowe, Caro, Kerrow, Karrow, etc. My own surname of Carah is Cornish and is a derivitive of Caro and before that Carro.