Do Objective-C Category names do anything?

Question

A class can be extended in Objective C using a category such as:

@interface NSString (CategoryName)
-(NSString *)myFabulousAddition;  // a fabulous additional method
@end

/////////////////////////////
@implementation NSString (CategoryName)

-(NSString *)myFabulousAddition {
    // do something fabulous...

}
@end

In this small example, I would be adding the method myFabulousAddition to NSString. I could then call it by [anNSString myFabulousAddition] just as if it were part of the NSString set of methods. Great and useful.

In the Apple documents regarding Categories, the docs state:

There’s no limit to the number of categories that you can add to a class, but each category name must be different, and each should declare and define a different set of methods.

What if you have something like this:

@interface NSString (CategoryName)
-(NSString *)myFabulousAddition;  // a fabulous additional method
@end

@interface NSString (ANOTHERCategoryName)
-(NSString *)myFabulousAddition;  // a DIFFERENT fabulous additional method 
                                  // BUT with same name as the other category
@end


/////////////////////////////

@implementation NSString (CategoryName)

-(NSString *)myFabulousAddition {
    // do something fabulous...

}
@end
@implementation NSString (ANOTHERCategoryName)

-(NSString *)myFabulousAddition {
    // do something equally fabulous, but DIFFERENT...

}
@end

The lack of a name in the parenthesis indicates that the form is an extension to the class, like so:

@interface MyObject ()   // No name -- an extension vs category to MyObject
- (void)setNumber:(NSNumber *)newNumber;
@end

Does the category name have any meaning to the compiler or linker? Is the category name part of the method signature in anyway or is it part of a primitive namespace? If the category name is meaningless, how do you know if you are about to stomp on another method and get undefined behavior?