T or P?
The transcription of the second to last letter as T, found in Janssen and the CIL, is a misreading of the actual letter P. The mistake is easily made, as the round shape of the original letter has faded.
In conclusion, we cannot determine the real name of the boy. I like to go for Licisippus. But whatever variant one may read, all names are unusual. I have found no other instance of any of them. It might be so that the parents had romanized his original Punic name.
The problems in reading the boy's name indicate that the mason had quite some trouble in carving the text. We can also see him struggling in other parts of the inscription.