To answer your question. Yes, the royal house/Imperial dynasty has to be in a position of power, like the House of Stuarts continuing to rule the UK or Valois in France. That brings me to the other part of your question, as I'm aware that many people today have ancestral connections to these houses and dynasties. The goal here is to keep a direct line where they still have the name like "Valois, Tudor, Vasa, Rurik, etc", otherwise this thread falls flat as some of the current monarchs today (Looking at you UK) are descended from these branches.
That makes sense and thanks for clarifying.
A surviving Achaemenid Dynasty still ruling a Persian Empire after over two and a half thousand years would be amazing to see.