I'm not sure why you think "Alexander" sounds wrong. That is indeed what his bodyguards and officers would have prided themselves in calling him. Both "chief" and "my king" are completely unhistorical and wildly out of place for the setting.

Macedonian kings held a hereditary position, but still had to be formally "acclaimed" by the Assembly, which consisted of all adult male Macedonians in arms. This meant that the Macedonian army was formally the kingmaker, and that the authority of a king like Alexander rested on the consent of his troops. One consequence of this unusual relationship between king and army was that Macedonian kings deliberately cultivated an approachable manner. They were known to dress simply, to eat and drink the same fare as the men, and to demand no special rituals or forms of address. To keep on the good side of the men who had risen them to the throne, they tried to profile themselves as "one of the boys".

This went double for the bodyguards of the king. As a rule, these were members of the most powerful Macedonian noble families. Most of them had grown up together with the king in the Macedonian elite education system. Several of them may have been the king's romantic or sexual partners. Upon reaching adulthood, these men served together continuously as close confidants and companions in battle. They would not only address the king by his name; they would be outraged if they were told to address him any other way.

Alexander in fact got into trouble with his Macedonian soldiers for precisely this reason. Part of the struggle of his later reign was the need to unite two very different styles of kingship: the informal, first-among-equals Macedonian style, and the exalted, divinely-sanctioned Achaemenid Persian style. Over time, Alexander began to appropriate the customs of the Persian court in order to seem more kingly to his new subjects; this included the particular custom of proskynesis, or obeisance, which required those who approached the king to bow, kneel or even prostrate themselves before him. When the Macedonian officers learned of this, they lost their shit. To them, it was not only unacceptable and ridiculous but outright sacrilegious to treat a king with the kind of deference suited to gods (in Macedonian custom). They did not follow their king out of obligation to some exalted creature; they followed the man they could look in the eye and call Alexander.

Non-Macedonians, especially those from the rest of the Persian Empire, would have been more likely to address him with "O King" - the notion of personal allegiance expressed with the genitive ("my king") is alien to the ancient world.

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