Even though the title reflects the village name and the incidents happening in the village, there is much more symbolism in the name. The name is a double entendre.
The film makers could have selected another name like Ramapuram or another name like Subramaniapuram (another periodic film) but chose Rangasthalam.
Let us see what the word means. Rangasthalam in Telugu means a theatre stage where dramas are played or puppetshows are plated. Characters on a stage are actors. The plot a play goes according to the script written by the director and hero gets the most importance. So, the director means that the citizens in the village Rangasthalam are mere actors without having importance. They live (act) according to the orders (script) by the president of the village. Hence the film director is hinting it's a drama where the story goes according to the will of the president.
The protagonist (Ram Charan as Chitti Babu) is the narrator in the film. He introduces important characters of the film. He introduces the president of the village. He has been elected unanimously for 30 years. He is treated as a demigod. Whenever there's election, no candidate nominate themselves. When he submits his nomination, it celebrated like a fair. His judgements are obeyed like a decree. That is the respect they give to him.
[Spoilers ahead] After some incidents the protagonist and his brother come to know that the president who is revered is the bad guy.. They come to know that he has been dictating people on what to do (like a director does to the actors). They decide to contest in the elections against the president. After some events, the protagonist comes to know the unanimous victory is because the president kills his opponents. He meets a character named Ganapati Mama who once tried to contested in the elections. The goons of president tries to kill him but he escapes somehow. He says following words to Chitti Babu ( translation)
There are no heroes in this Rangasthalam. There's only one villain who is president.
When he uses Rangasthalam, he means a theatre stage as well as the village name. He says that what they think and what happens in the reality are totally contradictory. He says the citizens are living without knowing they are dictated. So, this is directly hinted in the film. That's the reason the film makers named it as Rangasthalam.
This is further hinted in the title song of the film (rough translation).
In this rangasthalm, even though there is no makeup and flashy costumes ( like a drama), we are toys. We are puppets. We are puppets played by an invisible hand. We are puppets dancing to a tune which no one can hear.
This song is played when the president submits his nomination. Here, the unseen hand is the president and the puppets are villagers. By saying a song which no one can hear, there is a hint of hero's character. In the film, protagonist Chitti is a person suffering from partial deafness. In this song, the director tried to give the story line of the movie.
By naming the title as Rangasthalam, the director indicates that the village is a stage. Villagers are the actors. He is hinting the story of the movie.
Naming it as Ramapuram or Krishnapuram which are popular names would not serve the purpose of saying the story of the movie and characters. That is the significance of the title Rangasthalam.