When it says "this card's name is treated as Harpie Lady" It means that. so the same way you can only have 3 copies of a single card you can also only have 3 copies of Harpy Lady. Which because Harpy Lady 2 and 3 are still technically named Harpy Lady, they all share those same 3 slots.
Harpie Lady, Harpie Lady 1, Harpie Lady 2 and Harpie Lady 3 are always considered 'Harpie Lady' even outside of duels. There are other Harpie cards that have a similar effect. Harpie Queen and I think also Harpie Channeler are only considered Harpie Lady while on the field or Graveyard, like Gemini monsters.
There is a work around you may add 3 Harpie queen along with your three Harpie monsters as Harpie Queen is only treated as Harpie Lady in the field and graveyard not the deck like Harpie Lady/ Harpie 1 2 3 and Cyber whom are considered Harpie Lady in deck field and graveyard