We've done this for our last two cruises because we knew our server would be on the ship. We made the request when we booked the cruise, but we also went to Rockn' Bar D (Magic) after we boarded just to make sure our request was made in person. On each cruise we got the server we requested.
Yes! You can in fact request them at the time you make your reservation. It is not always honored at that time however. You can go to wherever they have set up for Dining changes on the afternoon that you board, check if you have gotten your request, and if not ask them to change you at that time. Every time I've done this we have been happily accomodated, and it has lead to some very nice realationships that we maintain outside of cruise times as well. So don't hesitate to request!
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