Ah, that makes sense. Perhaps have it use the contentId for the new thread so it'll always show the new thread name? I'm not sure if something else is using the contentId for this specific AlertHandler though. Just a thought
The problem is most content types by nature only support a single piece of content, so in the context of a handler we only fetch that content; which in this case is the source thread. Everything else is cached and accessed in the template as extra data when needed - we don't do anything in the handlers which is action specific or with the extra data so ultimately this is as designed / design issue I think.
These alerts represent "snapshots" as they aren't attached to the content to avoid permission issues (and potentially misleading avatars). As such, this would really be as designed, as Chris suggested.