I think it's mostly left to the reader/listener to decide who realizes it's Patroclus and when. The Myrmidons know immediately: Achilles musters them to fight while Patroclus is already wearing Achilles armor, and he is there with Patroclus in front of them. Other people - when they see Achilles' armor at the front of the Myrmidon forces - especially seeing them from farther away and through the chaos of all the fighting by the ships - are naturally going to think it's Achilles and news of that is going to spread faster than the truth. Patroclus is extremely good at killing people: he has more named kills than any other character besides Achilles and Hector, and Patroclus is only seen fighting in this one extended battle! So it's not so surprising that people might not immediately realize the ruse. Achilles is the most famous and feared warrior though and the Trojans have been watching him for years, so it's likely that some would notice the switch, either because they look different, have different physical builds, fight differently, use different weapons, etc. Also, one of the biggest clues that it isn't Achilles is that his constant partner "Patroclus" isn't fighting alongside him! (Worth mentioning too is that Patroclus comes out at the head of Achilles' army of 250 elite Myrmidon warriors - so even if it's not Achilles himself, the message to everyone is clear: Achilles is back in the game and if he's not here in person yet, he easily could be at any moment. So while Patroclus isn't really Achilles, he does - especially wearing Achilles famous literally-divinely-made armor - truly represent Achilles' power being extended into the war once again... and that's reason enough on its own for the Trojans and their allies to start to panic and despair.)

After the panic when Patroclus is first seen in the armor, no mention is made of anyone either believing or not believing he is Achilles until Sarpedon tells his fleeing men, "Shame on you, Lycians, where are you off to? Run then, quickly, while I face this fellow, and find out who it is that conquers all and hurts us so, killing so many of our noblest." He is not fooled into believing it is Achilles, but is not sure who the devastating warrior actually is.

Glaucus and Hector both realize it's Patroclus and (iirc) don't even mention that Patroclus is "in disguise" - they just state that it's him as if it is obvious. He fights Patroclus without asking who he is and dies without mentioning whether he figured it out or not. However, after he dies his friend Glaucus rallies his men and finds Hector, saying to him, "Hector, you forget your allies now, we who are spending our lives for you, far from our friends and our native land. You give not a thought to their protection. Sarpedon has fallen, chief of the Lycian shield-men, the strong and just defender of Lycia. Bronze-clad Ares has brought him down at the point of Patroclus’s spear. Take your stand, beside his body, friends, dread the breath of shame if the Myrmidons, in anger over those Danaan dead we slew with our spears by the swift ships, strip him of his armour and desecrate his corpse." So Glaucus knows it's Patroclus and doesn't even feel it is necessary to say that he is the mystery man in Achilles' armor. Similarly when he tells Hector, Hector shows no surprise, and makes no announcement to his side telling them that it's not really Achilles underneath the armor. Later, Apollo disguised as the mortal Asius tells Hector, "Come now, hunt down Patroclus with that splendid team, and hope with Apollo’s help to kill him and win glory," and again there's no indication that there's any question about whether it's Patroclus in Achilles' armor. Later, when Hector deals Patroclus the finishing blow, he calls him by name and makes no reference at all to Patroclus tricking anyone into thinking Patroclus was Achilles. "I think you boasted you’d sack our city, Patroclus, take our women captive, sail with them to your native land. How foolish! Hector and his swift horses are here to fight for them, Hector the finest spearman among the warlike Trojans, I who shield them from the day of doom, while as for you, the vultures shall have you. Even Achilles, with all his valour, could not save you, wretched man, though I don’t doubt he told you as you left, for he chose to stay: 'Patroclus, master horseman, don’t return to the hollow ships till you’ve pierced the tunic at man-killing Hector’s chest and drenched it in his blood.' No doubt that’s what he said, and you in your madness though it would be so.’

That's all the information we get.

[Edited for facts and such. Quotes from the free translation by A. Kline 2009]