I propose we either stick to the name House of States or choose a different type of name such as House of Councillors. When referring to ‘The Senate’ one can easily confuse it with the U.S. Senate.
Moreover, ‘senate’ is derived from Latin ‘senex’ – old man, and the current draft foresees women of thirty years in this institution.
I like (Federal) Council or House of Councillors because its overall task is to oversee and guide the legal process with advice. House of States is also fine because it describes where it derives its power from.
But ‘Senate’ is a word from a different age in my opinion.