Lots of times I will use a different credit card on check out from the one I use to guarantee the room with, or when I check in. There may be a problem if you do not tell this to the desk clerk when you check out, because there is a process they do to remove the "hold" put on your credit card when you check in. While I am not exactly sure how it works, when they take the imprint, they authorize from the credit card company, a certain amount generally equal to the room rate times the number of nights plus a few dollars/pounds/yen/francs more for incidentals. This does not get charged to your account immediately, but the amount is "reserved" for the hotel. Should you have a credit limit on your card, and this "hold" maxes it out, you may find you cannot use your card elsewhere as long as the "hold" is on it.
I changed Amex cards on a stay last weekend and the desk clerk merely asked to run the original one through again, entered a code, and processed a "credit" note. He then gave me originals of all the credit card slips except for the final one, for which I received the normal customer copy.