Good questions. I think it may depend on the interpretation of the museum. For example, Buffalo Creek & Gauley #13 was a former New York Central engine. It is now privately owned(Ohio Central), but if it were going to a museum, I would think it could go either way. If a group that was trying to preserve New York Central Heritage got it they could preserve it as NYC. As it is now it is neither, but sits outside with Ohio Central on the tender!
As for coaches, and other rolling stock, I think it is open to interpretation. There is a good case to be made for equipment being left in its LAST color scheme, especially if its a class one railroad. I think a museum might prefer to have a more recognizable name unless the other name is a rare one!! I guess its open to interpretation, and no set rules!
Just for example, say someday the C&TS ceases to be in existance(I know perish the thought). So they sell off all the engines. I think it would be more likely the engines would be lettered as Rio Grande, than Cumbres and Toltec in some museum, don't you! But yes, the C&TS is what they have been lettered for the past 33-34 years. Eventually they will be C&TS longer than Rio Grande, but that doesn't mean its right! Just my opinion again!
Greg