No, none of the .NET languages support anything like this. This could be implemented by one of the compiler teams but I doubt they would ever do it.
As to how this could be implemented by you (not by the C# compiler team) would be to store all of your variable variables in a Dictionary<String,Object>
- this would allow you to associate a string with an object.
I have never really understood what problem is solved by variable variables (in other words, I have never heard a good argument for needing to use them). I would be interested to see an example where they were needed as I would imagine it wouldn't be too hard to find a better approach to solving the problem without variable variables.