So, you're basically saying that when you throw away or replace the last part that was a part of the original. The object is no longer the same.

I can kinda see where you're coming from with that point of view. There's likely some lingering sentiment when you replace that final part. And after it's replaced one could consider the end product a completely new item.

Also regarding clans. Personally, I think it's what the clan is known for that has to stay for the clan to be the same. If a clan is known for certain members, then after those members leave I could see myself not considering the clan the same clan as it used to be. On the other, hand if a clan is known for being comprised of players that are unreasonably talented at playing relaxed, and that quality stays the same. Then I would say the clan is the same clan it once was.

All depends on how strict you want to be with definitions. My car stood outside overnight and rusted a tiny wee bit. Is it still the same car? No physical object stays absolutely the same from one second to the next. Change happens, even if only on atomic and sub-atomic level. But our everyday notion of identity is lax enough that we don't assign things a new identity unless the changes are very noticeable to us. In case of a car having had its parts gradually changed, I'd say it's still the same car.

enough literature about this problem exists, this is semantics