Those are Persian kings in that passage. They’re not Greek kings. Don’t confuse them with the four horns.
When Daniel 8 talks about the 4 horns, it’s talking about Greek kings. The prominent horn is Alexander the Great. You got that right. He defeated the Persians. Then the horn is broken off, meaning Alexander dies. Then four horns grow up in its place. Meaning Alexander’s 4 generals take over the Greek empire, and make themselves kings over 4 sections.
Seleucus, Ptolemy, Cassander, and Lasymichus. Those were Alexander’s generals who became kings.
Prolemy was over Egypt (king of the South), and Seleucus was king of most of Asia (King of the North).
This is fulfilled in 1 Maccabees chapter 1.