A few months ago, I was in the same boat, although I only wanted to reserve 3 rooms. Asked Hyatt Concierge on Twitter and was told to make 3 separate reservations or 2 reservations, one for 2 rooms and the other one for 1 room.

In the end, I made 3 separate reservations with 3 separate confirmation numbers all under my name, and emailed the hotel directly to link these reservations.