switch over value of enum: case expressions must be constant expressions

I have an enum with the following structure:

public enum Friends {
    Peter("Peter von Reus", "Engineer"),
    Ian("Ian de Villiers", "Developer"),
    Sarah("Sarah Roos", "Sandwich-maker");

    private String fullName;
    private String occupation;

    private Person(String fullName, String occupation) {
        this.fullName = fullName;
        this.occupation = occupation;
    }

    public String getFullName() {
        return this.fullName;
    }

    public String getOccupation() {
        return this.occupation;
    }
}

I would now like to use switch to determine, if a variable name is associated with a certain enum:

//Get a value from some magical input
String name = ...

switch (name) {
    case Friends.Peter.getFullName():
        //Do some more magical stuff
        ...
    break;
    case Friends.Ian.getFullName():
        //Do some more magical stuff
        ...
    break;
    case Friends.Sarah.getFullName():
        //Do some more magical stuff
        ...
    break;
}

This seems perfectly legal to me, but I'm getting the error case expressions must be constant expressions in Eclipse. I can get around this with a simple set of if statements but I would like to know the reason for this error and how things might go south if this was allowed.

NOTE: I cannot change the structure of Friends