A contemporaneous Rome report placed the Ocean's Twelve actors at Hotel de Russie, while TravelMole directly says George Clooney stayed there and Lonely Planet independently identifies him as a hotel guest.
George Clooney stayed at Hotel de Russie in Rome while Ocean's Twelve was filmed there in June 2004. Contemporaneous reporting placed the film's actors at the hotel, and later independent hotel and travel coverage directly identifies Clooney as a guest during the production.
Source conclusion:
The cited sources support a stay at the named hotel.