What became of Chileab ben David HaMelekh?

Question

What became of Chileab ben David HaMelekh?

Shmuel II - II Samuel - Chapter 3:3 And his second, Chileab, of Abigail the wife of Nabal the Carmelite; and the third, Absalom the son of Maacah the daughter of Talmai the king of Geshur.

and his second, Chileab of Abigail: Elsewhere the Scripture calls him: “And his second, Daniel” (I Chron. 3:1). Said Rabbi Isaac: Since the scorners of the generation were saying that Abigail was pregnant from Nabal, his features were changed, so that he resembled his father. And our Rabbis said that he would embarrass (מכלים) Mephibosheth in legal matters.

https://www.chabad.org/library/bible_cdo/aid/15863/showrashi/true

What became of Chileab ben David HaMelekh? Did he serve in Shlomo's kingdom? As per Rashi, how did Chileab ben David HaMelekh "embarrass (מכלים) Mephibosheth in legal matters"? Why is he called "Daniel" in a different passage, I Chron. 3:1? Where does Rashi source his answer to this last question?

Answer 1

Refer to Gemara Brachos 4a:

It was taught in a Tosefta from a tannaitic tradition: His name was not Mefiboshet, but rather Ish Boshet was his name. Why was Ish Boshet referred to as Mefiboshet? Because he would embarrass [mevayesh] David in matters of halakha. According to this approach, Mefiboshet is an abbreviation of boshet panim, embarrassment. Because David was not embarrassed to admit his errors, he merited that Kilav (Chileab), who, according to tradition, was exceedingly wise, would descend from him. Rabbi Yoḥanan said: His name was not Kilav; rather, his name was Daniel, as it appears in a different list of David’s descendants. Why was he called Kilav? Because he would embarrass [makhlim] Mefiboshet, the teacher or authority figure [av] in matters of halakha. (Sefaria translation and notation)

So the embarrassment of Mephiboshes was that Kilav was so wise that he would put him to shame in areas of Halacha, and indeed Daniel was his name, but this is an alternative name which was based on his wisdom as explained.