Among the sons of the kings of Israel and Judah, it was the rule, rather than the exception, for the biblical writers to name only the son who succeeded to the throne. David's sons were a notable exception, because his life is told in great detail. A similar example is found with Ahab of Israel, the most famous and wealthy of the northern kings. His son Ahazaiah was reportedly one of 70 brothers (2 Kings 10:1), but none except Ahazaiah is named.
It is alo notable that among Solomon's many wives, only Rehoboam's mother, Naamah, is named. The same pattern follows here: only the mother of the next king is mentioned. It continues with Jezebel, the most famous Queen of Israel. None of her sister-wives is named although her husband had 70 sons.
Interestingly, two of Solomon's daughters are named. However they are mentioned not in their own right, but as wives to significant men:
Taphath -- married to Ben-Abinadab (1 Kings 4:11)
Basemath -- married to Ahimaaz, in Naphtali (1 Kings 4:14})
To the question of Solomon's other sons not being mentioned because they were victims of human sacrifice: this is more plausible than it may seem on the surface. In the biblical account, Solomon's kingdom was divided because he supported his wives' religious practices.
On a hill east of Jerusalem, Solomon built a high place for Chemosh
the detestable god of Moab, and for Molek [Moloch] the detestable god of the
Ammonites. He did the same for all his foreign wives, who burned
incense and offered sacrifices to their gods. (1 Kings 11)
We have already seen that Rehoboam's mother was an Ammonite. There is no indication that the above offerings included human sacrifice but this did reportedly occur in her country of origin. However, we know from the above that only the succeeding son was normally mentioned in the biblical account, so we should not assume Rehoboam "was the only one withheld from sacrifice." Solomon deserves as much as anyone to be presumed innocent of such a crime until proven guilty.
Queen of Sheba's son
About Solomon's supposed son with the Queen of Sheba, this is even more plausible, and it is accepted as fact by millions of Ethiopian Christians and others. The account in 1 Kings 10 gives more details about Solomon's relationship to her than to any other woman and speaks of her being "overwhelmed" by his court's magnificence. She solidified her alliance with him with an exchange of opulent gifts. If she had no daughters of her own to offer as a wife/concubine, as other monarchs did, it is not out of the question that she would seal the alliance by conceiving a shared child with him. The account concludes by saying:
King Solomon gave the queen of Sheba all she desired and asked for,
besides what he had given her out of his royal bounty. Then she left
and returned with her retinue to her own country. (1 Kings 10:13)
Whether such a child was actually born, his existence is definitely affirmed by literally millions of Christians.
Out of all the nations that claim her, she has the most profound
impact upon Ethiopians. For them, this mythical queen is the founder
of their Ethiopian civilization and one who's cherished and beloved by
their Christian population. Ethiopia's account of the Queen of Sheba
is seen as the first ancestor of Ethiopia's imperial kings, known as
the "Solomonic Dynasty". The Queen of Sheba is seen as the founding
ancestor of this imperial line and the beginning of Ethiopia's cherished
3,000 year historical claim. According to Christian Ethiopians, upon
visiting Jerusalem, Sheba was seduced by Solomon, and gave birth to
their son of Menelik. After Menelik grew older, he would end up
journeying back to Jerusalem to visit his father Solomon and
subsequently stole the Ark of the Covenant to Aksum, where it resides
in St. Mary of Zion Church.
However this is a matter belonging to Christian legend, not the biblical account.
To conclude, only Rehoboam was named as Solomon's son because it was the convention throughout the biblical account to name only the son who succeeded to the throne, with few exceptions. We should not presume human sacrifice was a factor in only Rehoboam being named. It is plausible but far from certain that Solomon conceived a son with the Queen of Sheba.