Why is Train Heartnet called Black Cat?
He called himself Black Cat because he brings misfortune. He also said to his victims I have come to deliver some bad luck before he kills them. 

The motive of the bad luck also is shown in his number (13) and his birthday (13.4.; 13 => number of bad luck in western countries, while the four is the number for bad luck in Japan). Also his name has 13 characters.