The simple answer is: no, none at all.

A few names that pop up in Greek myths dating to the classical period do also appear in Bronze Age texts, like the individuals named a-ki-re-u (*Achilleus) in KN Vc 106 and PY Fn 79.2, but they've got absolutely nothing to do with the legendary character -- they're both in the wrong parts of Greece, for a start, and they're not warrior-leaders -- any more than you'd mistake a Latino named Jesús for the Jesus.

There's a small but important complexity in addressing your question, in regard to the bit

contemporary to the supposed timeframe the events took place

The complexity is that no such timeframe exists. The timeframe you're presumably thinking of -- historical Greece around 1200 BCE -- isn't in the mythological sources. That's the invention of later chronographers, around the 4th-3rd centuries BCE, who concocted their own timelines to link legendary events to the events of their own time.

They did that because they assumed the legendary events were real in some sense. But once you abandon that assumption, the idea of a timeline goes out the window. Keeping it, or trying to reconcile it with what archaeology tells us about the Bronze Age, would be about as strange as trying to reconcile The Lord of the Rings with what we know of England's prehistoric past. It's just that the strangeness isn't quite as glaringly obvious.

Every aspect of the Iliad and Odyssey sets them in the contemporary world, that is, the world of the 7th century BCE -- the prominence of colonialism, assemblies, and Phoenician traders in the Odyssey; the weaponry and the cult of Ilian Athena in the Iliad. They're flooded with false archaisms too -- like the ethnographic layout of Greece, and the weird use of chariots and iron -- because they're set in a legendary past; but that legendary past is, in its fundamentals, built on the time when the poems were composed. Their setting is an archaified version of the 7th century BCE, not the real 12th century BCE.

We don't know how much about this time period we don't know. The number of written sources we have from the Mycenaean period is close to nonexistent, consisting of preserved clay tablets and jars, and contain mostly administrative data such as inventory lists. As is the case with most things recorded on clay tablets, they weren't meant to be permanent, but the clay was accidentally preserved when the building it was in burned. The closest we can come to saying that anybody in Homer's epics did or did not exist is that we at least know that 'Achilles' was a real name in use at the time (or rather, A-ki-re-u), not Homer anachronistically giving a modern name to a character of centuries earlier.

Not only can we not conclusively say whether or not any of the people involved existed, we can't say definitively that the war happened or not. By the 18th century, the consensus was that it hadn't. What they did acknowledge was that there was at least that the city of Troy (or Ilion, the city has been known by both names) existed, being mentioned in period texts we do still have, such as the records of the Hittites, although they were unclear on the location. In 1870, professional vandal Heinrich Schliemann working on a theory proposed to him by Frank Calvert, started digging underneath the ruined city of Hisarlik in modern-day Turkey, a ruined city built on top of another ruined city and so on and so forth over thousands of years.

Why do I call him a professional vandal instead of an archeologist, you might ask? Because Schliemann's 'archeology' toolkit included entirely too much dynamite and entirely too much willingness to use entirely too much of it.

Schliemann blasted his way past the layers of his dig site he deemed unimportant until he reached the layer he decided was the site of Troy during the war, but had destroyed countless archeological treasures on his way down, and had gone too far, blasting his way down to a layer a thousand years too early, this layer is now identified as 'Troy II' out of the 10 Troy layers at the site. The actual site most likely to be the city as of the Trojan War is Troy VIIa, which shows signs of having been invaded and burned approximately 1180 BC, corresponding chronologically with the Late Bronze Age collapse (starting approximately 1200BC), the beginning of the Greek Dark Age, and the fall of the palace system that Mycenaean political and economic systems were built around.

In short, we know that a city we think is in the right place to be Troy existed and was attacked and burned at what we think is the right time. Everything beyond that is questionable, especially any individual people.

Others have given a more direct answer to your question, citing the sources for Wilusa, the Ahhiyawans, and some of the personal names.

I think it is slightly relevant to your question to mention the Tawagalawa Letter and Piyamaradu, as in my opinion it corroborates SOME of what we can see in the Iliad, though very loosely.

The Tawagalawa Letter was sent by either Hattusili III or Muwatalli II (presumably) to an Ahhiyawa leader, asking for aid in dealing with Piyamaradu, who the Hittites labeled as a renegade for his anti-Hittite actions in Western Anatolia for a period of a few decades. He seems to have been from the nobility of the vassal kingdoms of western Anatolia and eager to press this claim, and to do so allied for some time with the kingdom of Ahhiyawa as the Hittites called it (and which there is great debates over what this identification means in terms of borders, organization, etc.)

While some have tried to argue that Piyamaradu might be a transliteration into Hittite of the Trojan name Priam, I do not find this compelling. However, the seemingly personal focus of his goals, and his individual attempts to pursue them within larger political backgrounds certainly do sound a little like the actions a Homeric hero might take or be offered; gathering up men to individually raid targets in the Hittite Empire, individually pushing his claims to land, whether legitimate or not, allying himself with different powers at whim…all sound like actions available to heroes on both sides of the Trojan war in the Iliad. For me, I always like to reference Piyamaradu because his actions embody how personal the politics of the “Trojan War” period likely were, and how loose political organization and alliances might be. And, like Homer’s heroes, Piyamaradu is mentioned at least a generation after his deaths as an infamous pirate and renegade, at least in Hittite records.

Whether Piyamaradu did it for glory, what he perceived to be his rights, or just because he wanted to is difficult to say without his input, which we likely will never have. But his actions do point to the fact that these sorts of rebellions and attacks by individuals could happen, especially in the west; though the Hittites, it seems, were usually pretty good at putting such enemies down.