You cannot have evaporative cooling without evaporating some water into the atmosphere.
A closed circuit cooling tower still has water spraying onto the closed loop process water heat exchanger coil and mixing with atmospheric air to evaporate and cool the process water indirectly instead of evaporating and recirculating the process water that doesn’t evaporate directly like in an open-loop cooling tower.
I suppose you could condense the evaporated water somehow by using a chilled umbrella or some other ridiculous contraption above the cooling tower, but why would you do that?
FWIW I sell and run commercial electrical work, primarily to mechanical contractors who are installing boilers, chillers, cooling towers, and pumps. I spend my professional life immersed in this type of equipment.