How to get the name given to transaction controller using beanshell preprocesssor in jmeter

You cannot walk further than Previous Result or Previous Sampler so I would state that it is not something you can implement easily. Looks like your test is not very well designed as normally people do not require knowing the name of the parent sampler controller.

Nevertheless you can get access to JMeter Test Plan Tree and figure out information from there. The example code will look something like:

import org.apache.jmeter.control.TransactionController;
import org.apache.jmeter.engine.StandardJMeterEngine;
import org.apache.jorphan.collections.HashTree;
import org.apache.jorphan.collections.SearchByClass;

import java.lang.reflect.Field;
import java.util.Collection;

StandardJMeterEngine engine = ctx.getEngine();
Field test = engine.getClass().getDeclaredField("test");
test.setAccessible(true);
HashTree testPlanTree = (HashTree) test.get(engine);

SearchByClass txnCtrlSearch = new SearchByClass(TransactionController.class);
testPlanTree.traverse(txnCtrlSearch);
Collection txnControllers = txnCtrlSearch.getSearchResults();

for (Object txnController : txnControllers) {
    log.info(((TransactionController) txnController).getName());
}

Demo:

Some information on using JMeter API from Beanshell scripts: How to Use BeanShell: JMeter's Favorite Built-in Component