The name he received on the night of the Great Renunciation
On the day the news reached him, Prince Siddhattha was about to enter the city.
The Jātaka commentary relates that King Suddhodana, hearing that Rāhula's mother had given birth to a son, sent word saying: tell my son of my gladness.
The Bodhisatta heard the message and spoke one sentence.
"Rāhula is born, a fetter is born."
The messengers carried that word back. The king asked what his son had said, and when he heard it, he declared:
"From this day let my grandson be named Rāhulakumāra."
The grandfather took the words his son had uttered in that moment and made them the child's name exactly as they stood. So the prince bore from his first day a name that means a fetter, and it was his own father who had first spoken it.
That very night the Bodhisatta resolved to go forth. The commentary relates that after sending Channa to prepare the horse, he thought he would look at his son first; so he rose from his seat, went to the bedchamber of Rāhula's mother, and opened the door.
Inside, a lamp of scented oil was still burning. Rāhula's mother lay asleep with one hand resting on the head of her son, on a bed strewn with jasmine.
The Bodhisatta stood there with his foot on the threshold and did not step in. The commentary records his thought at that moment: if he were to lift the queen's hand away in order to take up his son, she would wake, and then an obstacle to his going would arise.
"Even after I have become a Buddha, I shall be able to come and see my son."
Having thought only this, he went down from the palace.
The same commentary also notes that the statement that Rāhulakumāra was seven days old that night is found in the Jātaka commentary but not in the others.
The prince knew nothing of what happened in his room that night. As for what his father resolved on the threshold, it would come true seven years later.