Call your character by name, if that name is known to the narrator. Calling him "dark haired man" in one sentence, "the butcher" in the other and "the other man" in the third will confuse the hell out of the reader. It will lead the reader to believe there are three characters here, not one. Even if you refer to him as something else just once, it can still be confusing (just the other day someone here mentioned that he read the character being referred to as "the redhead", and he ended up going through the previous chapters trying to figure out if this was a new character or if the character in question really has red hair).
Instead of inventing nicknames for characters to avoid repetition, try arranging your sentences in a way that you don't need he/she. If the sentences are all of the same structure it doesn't matter how you call the character, they will still feel repetitive and monotonous.
Jack opened the door. He tiptoed inside. He was afraid he might wake up Marry.
It's not just that "he" keeps repeating, but the sentence structure is the same in every sentence. Boring.
Now imagine this:
Jack opened the door. The burly man tiptoed inside. The husband was afraid he might wake up his wife.
Can you tell me with absolute certainty how many people are there in the example above? And it still feels just as monotonous as the original example.
Instead, why not something like this:
Jack opened the door and tiptoed inside, afraid he might wake up Mary.
After opening the door, Jack tiptoed inside so not to wake up Mary.
Jack opened the door, then tiptoed inside. Mary was sleeping.
You can write these few simple sentences in so many interesting ways without using he/she, or at least reducing it.
If it just can not be avoided, I think a safe "formula" would be to call the character by name the first time he's mentioned in the paragraph, then "he/she" for the rest of the paragraph, or several more if no other characters are mentioned. When the next character is mentioned, use his name first and then "he" until another is mentioned and so on.
One way to keep the clarity is to make only one character perform the action per paragraph. For example, if Jack is opening the door, Mary is yelling and Steve is smoking a cigarette, they should all have their own paragraph for what they're doing, even if the paragraphs end up being no more than a short sentence. It avoids confusion. The same for dialogues, you should never have two people speaking in the same paragraph, that's confusing as hell.
Also, if you're writing from a close third POV, it largely depends on the POV character how the other characters will be referred to. For example, in Lois McMaster Bujold's "Mirror Dance", we have two POV characters, Miles and his clone brother Mark. When we see things from Miles' perspective, the character of Elena Bothari-Jesek is referred to as Elena, since Miles has grown up with her and was in love with her most of his life. When seeing things from Mark's perspective, she's referred to as Bothari-Jesek, as Mark barely knows her, and she also scares the hell out of him. In Miles' chapters his parents are referred to as "mother" and "father", in Mark's they're referred to as "Count" and "Countess" because in this book Mark meets them for the first time. This also serves as a reminder to the reader that even though Mark is impersonating his clone brother on and off throughout the book, he's a completely different individual.