PingPlotter does its lookup for a specific name at the time you start the trace. From then on, it uses that IP address, and only uses the name for informational purposes. Internally, PingPlotter keeps track of that target by IP address, rather than name - and there's no mechanism for changing the target's IP address based on a DNS change.
We're working on some future plans (still in the planning stage - nothing real yet) that would allow us to possibly handle DNS Name changes, although a lot of the current matching logic works based on IP Address, so it's not an entirely easy or obvious thing to do.
Thanks for your feedback on this. We've added your request to the related comments so we take it in to account as we work on this.