“It’s not their name to use.”
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You don’t understand. Whenever you make a political donation the political campaign collects certain data including your name AND THE NAME OF YOUR EMPLOYER. When I recently wasted my money by making several donations to the Moore campaign, that campaign’s donation page collected my employer’s name. I’m sure the Gillibrand donation page collects the same information AS REQIRED BY FEDERAL LAW.
By the way, if Moore sorted his campaign donations alphabetically by EMPLOYER I’m fairly confident that not a single item will list “Palo Alto High School” as the employer.