O.K. I had to do some fancy talking to pull this off. I am going to shorten this as much as possible, because it is a long story.
This is Basically what I did
1. Called and said I wanted to change the credit card, because mine was cancelled
2. said I was using my sisters card
3. freaked, but did not panic, when basically the last thing the CM said was that I needed a picture I.D. Kept repeating to myself just get the charge changed, you can figure out later... how to fix it.
4. Called back (somehow got a grand gathering planner

, maybe this was a blessing in disguise) I asked if she could transfer me to dining, she said she could help me.
5. Told her my "sister was cancelling her trip but I was not, However the ressie was under her name, but my credit card. Told her I did not want to lose this very hard to come by ressie, because I would not have a picture I.D. with my sisters name. Asked if she could change the name on the ressie, she said she could. and would. ( I could tell I had her a little bemused, by this whole conversation)
6. she looked up the confirmation # and told me it already had my name on it and not to worry
Whew, told you it was a long one!!! but, I pulled it off! I kept praying for it to work the whole time!!! that might have helped too, and I am not a holy roller, but do believe in prayer
Maybe this strategy will help someone else. You definately need the other persons, Name, phone # address, where they are staying and how many in their party. Although, I only needed her name and confirmation # all the other things were mentioned in the first conversation, I just said yes to everything she said, but if she had asked me a question, I would have been sunk.
The person who gave up the ADR's sole concern was her credit card, so I realized to break it down, and do one thing at a time, and it worked in my benefit. I had to do something similar, to score a hotel for my choice.
Hope this helped!!! I am not sure if I can get a BBB, but if someone is giving it up, you could hook up a 3-way call or I could call at specific time or try my above strategy.