gistfile1.m

-(void) initStringValue: (NSString *) newValue {
  myString = newValue;
}

-(void) changeStringValue: (NSString *) newValue {
  // Something needs to change here
  myString = newValue;
}

MyClass * objA = [[MyClass alloc] init];
objA.name = @"This is my name";

[anotherObj initStringValue: obj.name];

[anotherObj changeStringValue: @"This is someone else's name"];

// At this point, I would like objA.name to be set to "This is someone else's name".

Also check out the NSString API:
http://developer.apple.com/library/ios/#documentation/Cocoa/Reference/Foundation/Classes/NSString_Class/Reference/NSString.html

The stringWithString: method applies a copy to the string you're giving as reference:

• (id)stringWithString:(NSString *)aString
  Parameters
  aString
  The string from which to copy characters. This value must not be nil.

Brock I made a small test for something similar, and seems that it should work also for this.

NSString *stringA = @"hola";
NSString __strong **pointToStringA = &stringA; //The strong is because ARC can't determine who handle the memory for this pointer

NSLog(@"%@",stringA);
NSLog(@"%@",*pointToStringA);

stringA = @"boo";
NSLog(@"%@",stringA);
NSLog(@"%@",*pointToStringA);

2013-08-18 17:53:07.036 childViewController[2510:c07] hola
2013-08-18 17:53:07.861 childViewController[2510:c07] hola
2013-08-18 17:53:10.097 childViewController[2510:c07] boo
2013-08-18 17:53:10.694 childViewController[2510:c07] boo