Well Greeks certainly thought so. If you want to ignore things based not off Greek sources and instead external parallels you have Hittites. Who had multiple treaties with what they called "Wilusa" and it's not a stretch based on linguists to label that the same as what Greeks called Illium. There are also specific names like Alaksandu(Alexander) and an older letter of somewhere in the previous 30 years before that one that identifies the leader as Piyama-Radu(Priam). So there are corresponding names for the heads of state Priam and his sun Alexander/Paris(they are used interchangebly in Homeric Epic for the Meter) to their neighboring empire.

As for the Greek Side, there is in Linear B the name Akireu(Achilles.) So yes the names existed and were real people in some position to be mentioned in official heads of state. Far closer than say any evidence of Arthur Pendragon existing as some mythological version of Charlemagne that some argue.

There's another fun tid bit from Egyptian sources. The Egyptians of the Bronze Age during the era of the Sea People (who some scholars argue are Bronze Age Greek Mercenaries) called these foreign story tellers and bards/entertainers under a title called Hemera(Homer). So there was some kind of legacy or title where the Egyptians treated all foreign traveling storytellers the name Homer before the dark age of Greece was over and they rediscovered literacy and began writing down the epics.