Unless the two men are identical twins who also dress alike, and they speak and act exactly the same, there is some way to distinguish them.
Think about how you refer to people whose names you don't know in real life. You may use a capsule physical description: "the tall girl", "the bald man", etc. Not applicable to strangers met in a bar, but in other contexts I'll often describe them by some sort of role, like "my math teacher", "the guy from accounting", "the policeman", "my neighbor's brother", etc. If all else fails, you can always call them "the first man" and "the second man".
In most conversations, it isn't necessary to repeatedly identify who you're talking about. You might say, "And then the blond guy said ... and after that he ... and then I said to him ... and then he ..." etc. That is, the person quickly becomes "he" or her" or whatever.
If your characters are meeting these people, then in real life they would likely give their names early in the conversation. For a fiction story you might have them give names especially early just to avoid the problem you're describing.
If you talk about third parties in a context where your characters wouldn't learn their names, like if they're sitting at the bar talking about these two strangers they see across the room, in real life they'd likely quickly come up with short-hand descriptions or nicknames for each. Like they start out saying "the guy with black hair" but after saying that two or three times it would be as awkward in real life as in a story, so they quickly start calling him "Blackie". Or someone says, "Hey, doesn't his beard make him look like Abraham Lincoln?" and then the other person calls him "Abe" and they both laugh but then they start calling him that regularly.
In other contexts, I often fall into regularly talking about someone by a short name for their role. Like I call someone "the librarian" or "the HR guy" or whatever and then start using that regularly like it was their name.
Once the characters start using a nickname, unless it's very extreme in some way, it's easy for the narrator to start using it too. By "really extreme", I mean like, if one of the characters decides she really hates some guy and refers to him as "the Lying Scum", it would sound strange for the narrator to calmly use the same term. The easy solution is to avoid making up that kind of nickname. But for the characters to call someone "Baldy" and then for the narrator to say, "Then Baldy crossed the room and picked up a glass" or some such doesn't sound particularly strange to me. You might put the nickname in quotes the first time or two to emphasize that you're using a nickname, but then just drop the quotes.