Puppet

A puppet was a movable model of a person that was controlled by another person, typically with strings.

The Carrionite Lilith in 1599 used a wooden puppet of William Shakespeare to hypnotise him into writing Love's Labour's Won without his knowledge of having ever written it. (TV: The Shakespeare Code)

Ashildr made puppets. (TV: The Girl Who Died)

When was watching a television series, George Trenchard informed him that they were not actual aliens but merely a puppet show for children, to the disappointment of the Time Lord. (TV: The Sea Devils)