This is not a case where the government is telling employees that they cannot say certain things while on the job. That would be reasonable (see the Hatch Act, for instance, which the Trump administration violates constantly). It is compelled speech. They are sending out a message from that person without that person's knowledge or consent. The first amendment prohibits the government from forcing someone to say something that they do not want to say. That is true even for government employees (see https://en.wikipedia.org/wiki/Janus_v._AFSCME)