As the other answers state, the Lore was very much not present in the first game, but exploded in the second. The only hard link to any of the PCs actually being a character in the game's lore is Ogden's introduction:
Lore from the manual of Diablo II established that the warrior character from the first game was unknown to the village, despite Ogden apparently knowing him as per his greeting quote. The issue was 'solved' in a sense by lore developed for Diablo III, which established that the warrior was Aidan, known to Tristram, and thus apparently to Ogden as well.
So, this information was not present in the first game. The PCs were simply known as "the Warrior", "The Rogue" and "The Sorcerer". Their characters were then later added to link them to specific characters in the Diablo story.
Aidan; The Warrior
The "Hero that defeated Diablo" was retconned into Aidan; son of Leoric (Diablo's first victim) and brother of Albrecht (Diablo's initial vessel). Aidan had been sent to War by his father, due to his madness, and returned after Leoric's death, at the beginning of the events of Diablo 1. The idea is that he was the one that became convinced the only way to contain Diablo was to shove the Soulstone into his own head, which ultimately turned out to be Diablo's influence, making Aidan believe it to be that way.
The Warrior of Diablo I eventually became the Dark Wanderer that featured in Diablo II. Diablo III and supporting material altered his backstory to make him Aidan, the son of King Leoric. This was a retcon from previous lore, which established that the Warrior was a stranger to the people of Tristram.
Moreina; The Rogue
While Aidan was the one to become the ultimate victim of Diablo, turning him into his vessel, leading to the Events of Diablo 2, the others would not return from the depths of the Cathedral unscathed. The evil powers within the Cathedral were so strong that it ultimately affected the other two as well.
Blood Raven (originally known as Moreina) was a member of the Sisterhood of the Sightless Eye. She played a role in Diablo's defeat during the Darkening of Tristram, but fell into Hell's thrall in the aftermath.
Jazreth; The Sorcerer
While not corrupted in the same manner as Moreina (who was turned into a demon), Jazreth instead fell to madness, eventually becoming the Summoner in Diablo 2.
The Summoner (previously named Jazreth) was a powerful sorcerer. Once a member of the Vizjerei and opponent to Diablo, he fell to evil and was struck down by a new group of heroes.