How do I avoid over-using the garbage collector?
For the Garbage Collector, it doesn't matter at all. You don't create the object. You just use an object reference to it in the above code.

The String object itself is still stored in the Person class and is therefore not garbage-collected until it is changed inside the Person object, or the Person object itself is garbage collected (which will happen when the Person does not have any more references to it).

Normally, you don't need to worry about "over-using" the Garbage Collector.

However, for the sake of readability it is a good practice to declare the variable in the smallest scope as possible. Therefore, I would go with the inside the for-loop approach.