What is the story of Sage Dhaumya and his disciple Aruni? How did Aruni get the name Uddalaka?
The story of Sage Dhaumya and his disciple Aruni is described in Adi Parva of Mahabharata as below:
About this time there was a Rishi, Ayoda-Dhaumya by name. And Ayoda-Dhaumya had three disciples, Upamanyu, Aruni, and Veda. And the Rishi bade one of these disciples, Aruni of Panchala, to go and stop up a breach in the water-course of a certain field. And Aruni of Panchala, thus ordered by his preceptor, repaired to the spot. And having gone there he saw that he could not stop up the breach in the water-course by ordinary means. And he was distressed because he could not do his preceptor's bidding. But at length he saw a way and said, 'Well, I will do it in this way.' He then went down into the breach and lay down himself there. And the water was thus confined. "And some time after, the preceptor Ayoda-Dhaumya asked his other disciples where Aruni of Panchala was. And they answered, 'Sir, he hath been sent by yourself saying, 'Go, stop up the breach in the water-course of the field,' Thus reminded, Dhaumya, addressing his pupils, said, 'Then let us all go to the place where he is.' "And having arrived there, he shouted, 'Ho Aruni of Panchala! Where art thou? Come hither, my child.' And Aruni hearing the voice of his preceptor speedily came out of the water-course and stood before his preceptor. And addressing the latter, Aruni said, 'Here I am in the breach of the water-course. Not having been able to devise any other means, I entered myself for the purpose of preventing the water running out. It is only upon hearing thy voice that, having left it and allowed the waters to escape, I have stood before thee. I salute thee, Master; tell me what I have to do.' "The preceptor, thus addressed, replied, 'Because in getting up from the ditch thou hast opened the water-course, thenceforth shalt thou be called Uddalaka as a mark of thy preceptor's favour. And because my words have been obeyed by thee, thou shalt obtain good fortune. And all the Vedas shall shine in thee and all the Dharmasastras also.' And Aruni, thus addressed by his preceptor, went to the country after his heart.