Sandy posted the correct method (getFilesByName()) for the DriveApp.folder class.
A code sample would look something like this:
function fileChecker(){
try{
var folder1id = '';
var folder2id = '';
var folder1 = DriveApp.getFolderById(folder1id);
var folder2 = DriveApp.getFolderById(folder2id);
//get the files in folder 1
var files = folder1.getFiles();
// loop through the files in folder 1
while(files.hasNext()){
// get the individual file in folder 1 to process
var file = files.next();
// check for same name in folder 2
var files2 = folder2.getFilesByName(file.getName());
// the code below assumes there is only the potential for a single file
// in folder 2 with the same name as folder 1
// otherwise additional processing would need to be handled
if(files2.hasNext()){
var file2 = files2.next();
file.setTrashed(true);
// add the file to folder 1
folder1.addFile(file2);
// remove the file from folder 2
folder2.removeFile(file2);
}
}
}catch(err){
Logger.log(err.lineNumber + ' - ' + err);
}
}