There is no built-in way to do this that I am aware of.
You can create a powershell script that will recursively go through all of your content files, then use regular expressions to find the appropriate Content.Load functions in your code and replace those with randomly generated hashes. You would then run this script as part of obfuscation.
It would probably even be simple to write if you have all of your Content.Load<> calls in a single file. Then the pseudocode would be something like:
For All Files in Content directory (and subdirectories, recursively):
String hash = CreateRandomHash()
File.renameTo(hash)
"LoadContent.cs" = "LoadContent.cs".replace("Content.Load<Texture2D>(" + File.original.Name + ")", "Content.Load<Texture2D>(" + hash + ")");
But, you know, "pseudocode." :). It would take some work.