The film's official novelisation indicates that the frequency was reserved for Palpatine.
“Yes, sir.” A silent buzzing vibration came from a compartment
concealed within his armor. Cody frowned. “Go on ahead, General. We’ll
be right behind you.”
That concealed compartment held a secure comlink, which was
frequency-locked to a channel reserved for the commander in chief.
Star Wars Episode III: Revenge of the Sith
That being said, the Clones seem to accept the order from whoever is using the frequency without question, as a result of their training/brainwashing.
A holoscan appeared on the palm of his gauntlet: a hooded man.
“It is time,” the holoscan said. “Execute Order Sixty-Six.”
Cody responded as he had been trained since before he’d even awakened
in his creche-school. “It will be done, my lord.”
The holoscan vanished.
Star Wars Episode III: Revenge of the Sith