If you do nothing, Hilton won't cancel the overlapping stay, but you won't get points for one of them.
You can ask Hotel A if they would cut your existing reservation to 3 nights without changing the rate. Sometimes they have an "early departure fee" which they would charge instead of the rate for the 4th night, but you can negotiate this, particularly if they are fully booked they may not mind selling your unwanted 4th night for a higher price.
I didn't know you could do this. Makes sense if they are full they may be able to get a higher rate than the OP paid.
In relation to the question about cancelling and rebooking, yes you would have to pay the new rate.