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Balnea's full name is Balnea Thermaenni Caldarium. Balnea refers to the Latin word for bath, Thermaenni is likely a reference to thermal springs, and Caldarium was the name of the room containing the hottest water in Roman Baths, referring to the Thermal bath (examine text: "Have you ever been in hotter water before?").
Balnea is meant to be American, as Mod Michelle said in the patch notes that "Balnea from As a First Resort has had some spelling altered to reflect her American way of speaking."