Oh, I`ve got the solution:
Start line 1020:
var fileNameBody = fileNamePrefix;
//fileNameBody += "_" + zeroSuppress(i, 4); (change this line into a comment)
if(fileNameBody != '') fileNameBody += "_"; (make an if-statement for the case you give the file a perfix, it will add automatically an underscore)
fileNameBody += layerName; (say that the file name is the layer name)
done 