Yes, it holds "A Legendary Ocean" amount or water. (Couldn't resist).
When a card mentions that "This card's name is treated as [NAME]" that means that particular card can be used for anything that references the card name. It also means that when it comes to deck building you cannot have more than a grand total of 3 cards with the exact same name.
So with "Umi" / "A Legendary Ocean", you can 3 of 1, 3 of the other, 2 of 1 and 1 of the other, etc. But you can't have 3 "Umi" and 3 "A Legendary Ocean" since that would mean you would have 6 cards named "Umi".
Likewise, "Harpie Lady", "Harpie Lady #1", "Harpie Lady #2", and "Harpie Lady #3" all are named "Harpie Lady". So any of them can be on the field when you activate "Elegant Egotist" or any can be selected by the effet of "Birdface". However you can only have a grand total of 3 of the above (any combination) since they all have the same name: "Harpie Lady".
- A