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.
Nope, Harpie Lady 1, 2 & 3 AND vanilla harpie had always been considered as the same name so the same slot in deck building. They don't need to fix anything.
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
Harpie Lady 1,2,3 and vanilla all are treated as "Harpie Lady" at all times, including deck construction. Cyber Dragons and Blue Eyes only change names when in specific locations, such as the field or graveyard. Reading the card explains the card.