Why was he called "Dhul-Qarnain" (i.e. Owner of the two horns)?

This is a controversial issue, that there is not a definite known reason behind this. Some said: he had something on his head that looked like two horns. Wahb Ibn Munabih said: He had two horns of brass on his head. (This interpretation is very weak)
Some scholars from among the People of the Book (Christians and Jews)
said: This is because he ruled over Persian and Roman territories. It was also
said: that he reached the first ray of the rising sun on the east and that on the west and he ruled over all that was in between. (The latter opinion is more likely true, which is the saying of Az-Zuhari)
Al-Hasan Al-Basri said: He had two braids of hair that he used to fold up and thus was called "Dhul-Qarnain". And, Ishaq Ibn Bishr narrated that the
grandfather of 'Umar Ibn Shu' aib said: DhulQarnain, once, invited a tyrant king to the way of Allah. The king hit him on the head and broke one of his horns.
Dhul-Qarnain invited him again and the tyrant broke the second horn. Thus, he was called "Dhul-Qarnain" .
Narrated Ath-Thawri that 'Ali Ibn Abu Talib (May Allah be pleased with him) was once asked about Dhul-Qarnain. He replied saying: He was a rightly-guided and pious man. He invited his people to Allah, but they hit him on his horn (side of the head) and he was killed. Allah the Almighty resurrected him and he invited them again, again they hit him on his second horn and he was killed (for the second time). Allah the Almighty revived him and thus he was called "Dhul- Qarnain". In other narrations, it was narrated by Abu At-Tufail after 'Ali Ibn Abu Talib that he said: He was neither a Prophet, nor a Messenger, nor an Angel, but was a godly, pious worshipper.