Sir Arthur Evans named the Minoan culture after the King Mino, a mythical Cretan king who supposedly constructed the great labyrinth. This was later proved to be inaccurate and while Sir Arthur Evans’ restoration of the site of Knossos probably prevented it from becoming complete unrecognizable he took a lot of liberties. The restorations at Knossos especially in the throne room are wonderful to look at but give tourists a false representation on the culture.
Heinrich Schliemann believed that the Mycenae Citadel was the mythical home of the Greek king Agamemnon, who was responsible for starting the Trojan War. He believed that much of what Homer wrote was based in history. Homer associated Mycenae with gold and this drove him to want to find the city possibly out of greed. He ended up finding gold in grave circle A of the “Palace’. He often ascribed names from Homer with his discoveries. This could have just been a great way for him as a business man to generate interest and potentially more money in his finds.
In reply to sjsaccom I do believe that they both did this in order for them to profit from their discoveries more not because they believed that they were in any way accurate.