I typically respond to one of the "we're looking forward to seeing you" emails I usually receive a week or so before a stay. I just let them know I have multiple reservations. It's probably not necessary to do anything in advance at many properties, but I've been told it helps when rooms are blocked a day or two before arrival, which is often done at resorts and other popular properties.
Good point. If I get an email from someone at the hotel in the week or so prior to arrival (not the generic "Reminder" ones that get sent out automatically), I would mention if I had separate/consecutive reservations.