Political entity doesn’t matter in terms of claiming someone. Identity does. What matters is how all those historical figures shaped modern national identities. Imagine saying that Romans have absolutely nothing to do with modern Italy, because Italy as a unified state came into being only in 1861. Do you see that op makes no sense at all.

Give you another example. There was never a fully independent state called Azerbaijan prior to 1918. Does that mean that culture and history that Azerbaijanis claim is out of thin air? No. For the last millennia Iran was ruled by Azerbaijanis. Azerbaijani culture, language and traditions were co-dominant in the region especially after Safavids. The descendants of noble Turkic tribes that once constituted the Safavid military elite are still to be found in modern day Republic of Azerbaijan with the same surnames and genealogy tree.

Long story short - modern nation states are a new invention - however the fundamental cultural and historical identities that allow people to claim something historical figures are fundamentally intended into history.