They really have no way of knowing how long you have had your mug, unless you have the previous year's design. I guess it's really based on the honour system -- they could ask you to prove you had purchased them I suppose, but I've never heard of them doing that.
If you're doing a split stay, any CM will tell you it's fine to use the same mugs. Technically the signs, and the mugs, say that they are good for length of stay in the resort where purchased. But split stays are a special case and it's just common sense that you'd be able to use the same mug for your entire vacation no matter how many resorts you had stayed in.
You'll find more threads about this on the Resorts Board, not in restaurants, since they can only be used in the food courts at the resort where you're staying.
And I say your mug is your mug, regardless of where you stay and whose name the reservation is under.