Still ruminating on SS code names. Does the President get a vote in the selection of his code name? We know Trump is Mogul and Melania is Muse. If the first family do get to choose, maybe Hillary liked Evergreen because of the Striesand song.
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The White House Communications Department apparently selects the letter and submits a short list if two-syllable names to the candidate, who then picks one. The other family members will then also have names that begin with that letter.
I think the SS picks. Generally all members of the family have a name with the same letter. If IRCC. I suppose the family would have veto power if they hated the handle.