First you need to set a name for your Actor: (Actor#setName)
myactor.setName("myactor");
Then you can get all the Actors in the Stage this is in, like this: (Stage#getActors)
Array<Actor> stageActors = mystage.getActors();
Then, you can use Actor#getName to check all the Actors for that name:
int len = stageActors.size;
for(i=0; i<len; i++){
Actor a = stageActors.get(i);
if(a.getName().equals("myactor")){
//a is your Actor!
break;
}
}
But it would be easier and more performant if you kept a reference to all your Actors and use it instead.