Bishop Odo, the half brother of William the Conqueror.
We'll assert that as the answer in line with what modern scholars typically believe. There had been a French legend that the tapestry was commissioned by Queen Matilda, the wife of William the Conqueror. But analysis of the tapestry led scholars to conclude Odo was the more likely source of the commissioning. Odo became Earl of Kent after the conquest and served as regent of England at times when William was in Normandy.