The case of the three-year-old girl - known to the public by the nickname 'Victoria' - has become a focus for accusations of police misconduct in Myanmar, where the force remains under the control of the army under a transition to democracy.
Lawyers and journalists had tried hard during the trial to conceal the identity of the child and her family to protect their right to privacy.
Around 400 people holding the signs of "Shame on you Myanmar Police Force" and "Justice for Victoria" marched through the center of Yangon under a hot sun.
The child was allegedly raped at a nursery school in Myanmar’s capital, Naypyidaw, in May.
After a court ruled that a suspect arrested in the case was not guilty, police announced the name of the victim.
A police spokesman did not respond to requests for comment on the accusations of misconduct against the force.
A democratically elected government led by Nobel Peace Laureate Aung San Suu Kyi took power in Myanmar in 2015, but key institutions such as the police remain under military control and efforts to strengthen the rule of law have floundered.
Prominent lawyer Kyee Myint told protesters that the constitution should be changed to bring the police under government control."We need to continue working to get the truth revealed in this Victoria case and also need to take legal action against the police who revealed the information," he said.