Use arcpy.FeatureClasstoFeatureClass instead. You can specify the name and location of the output fc.
Sure there is a way
FeatureClassToFeatureClass(in_features=None, out_path=None, out_name=None, where_clause=None, field_mapping=None, config_keyword=None)
Notice the third parameter is out_name, this is where you would specify the featureclass name.