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".

Okay this is the thing.
Let's say we have this code:

self.myAString = @"boo";
self.myBString = self.myAString;

NSLog(@"A Pointer Value:%@", self.myAString);
NSLog(@"B Pointer Value:%@", self.myBString);
NSLog(@"A Pointer Address:%p", self.myAString);
NSLog(@"A Pointer Address:%p", self.myBString);

self.myAString = @"far";
NSLog(@"A Pointer Value:%@", self.myAString);
NSLog(@"B Pointer Value:%@", self.myBString);
NSLog(@"A Pointer Address:%p", self.myAString);
NSLog(@"A Pointer Address:%p", self.myBString);

self.myMutableAString = [NSMutableString stringWithString:@"foo-mutable"];
self.myMutableBString = self.myMutableAString;

NSLog(@"A Mutable Pointer Value:%@", self.myMutableAString);
NSLog(@"B Mutable Pointer Value:%@", self.myMutableBString);
NSLog(@"A Mutable Pointer Address:%p", self.myMutableAString);
NSLog(@"A Mutable Pointer Address:%p", self.myMutableAString);

[self.myMutableAString setString:@"ops-I've Mutated. Sexy!"];
NSLog(@"A Mutable Pointer Value:%@", self.myMutableAString);
NSLog(@"B Mutable Pointer Value:%@", self.myMutableBString);
NSLog(@"A Mutable Pointer Address:%p", self.myMutableAString);
NSLog(@"A Mutable Pointer Address:%p", self.myMutableBString);

and It gets this result:

2013-07-21 14:20:14.905 BrockTest[11678:c07] A Pointer Value:boo
2013-07-21 14:20:15.119 BrockTest[11678:c07] B Pointer Value:boo
2013-07-21 14:20:15.341 BrockTest[11678:c07] A Pointer Address:0x4794
2013-07-21 14:20:15.561 BrockTest[11678:c07] A Pointer Value:0x4794
2013-07-21 14:20:16.061 BrockTest[11678:c07] A Pointer Value:far
2013-07-21 14:20:16.209 BrockTest[11678:c07] B Pointer Value:boo
2013-07-21 14:20:16.399 BrockTest[11678:c07] A Pointer Address:0x47e4
2013-07-21 14:20:16.677 BrockTest[11678:c07] A Pointer Value:0x4794
2013-07-21 14:20:17.391 BrockTest[11678:c07] A Mutable Pointer Value:foo-mutable
2013-07-21 14:20:17.590 BrockTest[11678:c07] B Mutable Pointer Value:foo-mutable
2013-07-21 14:20:18.033 BrockTest[11678:c07] A Mutable Pointer Address:0x753cc30
2013-07-21 14:20:18.503 BrockTest[11678:c07] A Mutable Pointer Value:0x753cc30
2013-07-21 14:20:19.517 BrockTest[11678:c07] A Mutable Pointer Value:ops-I've Mutated. Sexy!
2013-07-21 14:20:20.167 BrockTest[11678:c07] B Mutable Pointer Value:ops-I've Mutated. Sexy!
2013-07-21 14:20:20.743 BrockTest[11678:c07] A Mutable Pointer Address:0x753cc30
2013-07-21 14:20:26.883 BrockTest[11678:c07] A Mutable Pointer Value:0x753cc30

In Cocoa we have inmutable and mutable classes. The first ones doesn't let you to change it's value, pushing you to create a new object if you want to update its value. The seconds, let you to update their value.

The NSString class, is an inmutable object. That means this:

NSString *myFooString = @"foo-string";

The compiler does this internally:
NSString *myFooString = [NSString stringWithString:@"foo-string"];

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