In Castlevania III, you play as Trevor, Simon,s father. You gain allies along the way that you can switch to play as too. One of these allies is Alucard. In Mirror of Fate, Trevor travels to Dracula's castle to defeat Dracula. He fails and is killed by Dracula. However, Dracula is shown that Trevor is Dracula's son, so he pours some vampire blood in Trevor's mouth, and later Trevor is awakened as Alucard. Trevor is Alucard. My confusion is how can Trevor, in III, team up with Alucard if Trevor IS Alucard? Unless Dracula turned someone else and named them Alucard.....

Well I think Trevor was hallucinating thinking that he was fighting along side with Alucard making the player believe they are two different characters. Alot of games use this technique to change up the story.

That is because the Lords of Shadow games are set in a different universe from the normal Castlevania series since those games are more of a re-imagining of the series. Alucard and Dracula's backstories are way different between the two canons.

In Classic Canon, Dracula's origin is told in the game Lament of Innocence, where he used to be a normal human until his wife died, so he blamed God for her death and tried to have his revenge by becoming an unholy vampire to gain immortality I don't know much else since I haven't played that game yet. Years later, according to Symphony of the Night's backstory, Dracula would fall in love with another woman named Lisa, who would eventually give birth to their Dhamipr (half vampire half human) son Adrian, eventually Lisa would be falsely accused of witchcraft and killed. Lisa's last wish for her son was that he did not hate the humans, as their lives are already hard enough, but when Dracula found out Lisa died, he was enraged and waged war against humankind. Adrian, not wanting to help In his father's plans due to his promise to his mother, decided to oppose Dracula, changing his name to Alucard, the reverse of Draclua in order to show his opposition towards him. Eventually he would meet up with Trevor Belmont in Castlevania III: Dracula's Curse, first attacking him and his ally, but after proving themselves formidable warriors, Alucard joins them to stop Dracula. Here, Alucard does not have blood relation to the Belmont clan and is a separate person from Trevor.

In Lords of Shadow Canon, however, Dracula was originally a human named Gabriel Belmont, who's wife had died, but unlike Classic Canon, instead of cursing the name of God, he went on a quest to fight the Lords of Shadow, and find an artifact that would bring his wife back from the dead, I don't know much about this story, but I assume you pretty much know what happens in LoS and LoS: Mirror of Fate. Here, Trevor is the son of Gabriel, who becomes Dracula, who later turns Trevor into a full Vampire and renames him Alucard to show that he and Trevor are opposites of one another.

I hope this helped.

I never really thought about the two series being different universes, but yea, that makes sense. Thanks!