Meiko is gifted her private island by Tataru between 6.0 and 6.1 (as opposed to post-6.1), and eventually decides she wants to name it something close to Elpis II, similar to how she named her sailboat Amaurot. Elpis II or New Elpis doesn't quite sound right to her for an island name, however, so she ends up seeking out Erenville to ask what the plural of Elpis flowers are.
Elpae is the term he provides, and so she takes that for her island's name.
A'kihiko was, of course, offered a private island as well -- he was supposed to share it with Meiko -- but he politely declined, as he said he likely wouldn't have the time or attention span to properly maintain it. Of course, Meiko said he's always welcome to visit when he needs to get away. It as just as much his sanctuary as it is hers.
Upon discovering that the mammets on the island had blueprints available to build a tree house and other small abodes, Mei asked Remke ( @vieranbow ) if she would like to move to the island. This was mostly out of low-key paranoia considering all the danger Eorzea/the Scions/anyone Meiko cares about often faces. Remke agreed! She also went on to explain to Meiko that, per Viera tradition, this change of home would prompt her to change her surname as well.
So from post-Endwalker on, Remke Hyskel is known as Remke Elpae.
Meiko would eventually offer a place for her parents to live on Elpae for the same reason, but they prefer to use it as an occasional vacation home or sanctuary instead; they intend to die in Wadewick, is what they actually said. A bit grim, but understandable.
Meiko has offered at least temporary lodgings to all of her friends, but only her retainer Bomorhi Ura (@aurigold) has taken her up on it.
