Welcome, Jayako! That is indeed what is often called a 'nobile-type' hybrid, though (without looking it up to confirm) I think the particular cross you have is mostly derived from Den. moniliforme. I have a similar hybrid, Kokomo, very easy to grow and bloom and smells fantastic. I'd probably wait until late winter or early spring to separate them, that's when they should be initiating new growths/roots and will establish fastest if transplanted then.
When repotting, soak the whole pot in warm water for a few minutes, then work your finger down the inside edge of the pot to help pry out the plants together. Turn them out onto some clean newspaper and gently sort through them, being careful not to break roots if you can help it. You may want to keep very small ones together longer, otherwise just mount on wood or pot into small pots with a fast-draining mix, keep well-watered in bright shade in summer and slightly drier and brighter when the weather cools off. Hope this helps!