I\'m risking it this might be a newb question but here goes. I\'m tempted to add a method to a class that could possible have thousands and thousands of instances in memory
You don't need a method "Rename" at all; you already have one, it's the setter of the Name property. Instance methods do not require more and more memory on a per instance basis, that would be silly.
Don't make design decisions like this before profiling your code. Adding an instance method to a class is not going to cause a performance bottleneck, and even if it did, you shouldn't start out with a bad design based on a guess; prove it is a bottleneck and make adjustments as necessary.