Yes her palace is also called Inanna, but it is located on the mountain Ahvaz, not another dimension.
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She basically named her temple after her original name, that's all about it.
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Like, right now we have no idea how exactly the realm of the god works. Is it a place where all gods of all religions gather (Hakuno just linked there and chose Venus power so it's might be this but idk, he might linked to the realm of the Greek gods for example) and each of them have their own house (like Inanna for example would have her temple there), or they have their own realms like their respective legends (the encounter of Hakuno with Amaterasu described the place she's in with words describing Takamagahara, but in Shinto legend all of them kami should be in Tokoyo no Kuni).