Why does Benedict's pit boss think Lyman Zerga is legit because he hasn't heard of him?

He doesn't

You asked

why would "not hearing of him" lead Walsh to believe that Zerga is legit?

But it was not the point of their conversation. As you should know, Arms dealers work in secret, if not their work will be terminated and they'll go to jail, or worse. So what they meant by saying "That's why I don't doubt it.", That means if Lyman Zerga is anonymous entity in arms dealer's world, then He must be very good at what he does.

No indication about him being legit, but only he may actually being good in that kind of business. May be Zerga has cover ups, some legit businesses to cover up how he actually earns his money. Walsh must have searched them all and considering all the facts that he said he didn't doubt Zerga's story. There was never been any indication of Zerga being legit in this conversation.

You are misparsing the sentence.

That's why I don’t doubt it.

^{(emphasis mine)}

What is it in this sentence? It, as a pronoun, has an antecedent, the thing it refers to. Typically, as is the case here, a pronoun’s antecedent is the most recent thing mentioned that the pronoun could refer to, here that Lyman Zerga is

One of the biggest.

Benedict and Eddie aren’t discussing whether or not Lyman Zerga is actually a businessman, rather than a scam artist. That possibility doesn’t seem to have entered into their minds.

Rather, they are discussing whether or not Lyman Zerga is actually a big enough deal to justify a private meeting with Benedict. Benedict is a powerful, wealthy, important man—particularly in his own opinion. His time is valuable, and more than that, he is not the kind of man who gives away personal favors, such as a private meeting, to anyone who asks. In fact, he is the kind of man who gives personal favors only to the absolute highest echelons of society.

So Benedict’s concern here is whether or not he should spend time on a private meeting—if Zerga isn’t a major player, doing so is a waste of time and makes him look foolish. But if Zerga is one of the few people important, powerful, and wealthy enough to be worth meeting with, refusing a favor, particularly a relatively minor one, could be a considerable offense. If Zerga is the kind of person Benedict wants to meet with, he’s the kind of person who talks to people Benedict wants to meet with. Having such a person saying good things, feeling gratitude towards Benedict, is important and valuable to him. Snubbing him could tarnish his reputation. But being important and powerful himself, he has a lot of people asking for his time; he has to make sure he gives it to the right people.

This is the kind of calculation that Benedict has to make constantly, all day every day. Providing him with the information necessary to make that kind of call correctly every time is literally why Eddie has the job he does. Based on his contacts, Eddie understands that Lyman Zerga is a businessman, mostly dealing in arms. This much isn’t being questioned. The question is whether he is “one of the biggest.” And in the arms business, the biggest arms dealer you’ve heard of is almost-certainly not one of the biggest out there—the really big movers in that field keep themselves anonymous. Or, at least, so Eddie believes.

why would "not hearing of him" lead Walsh to believe that Zerga is legit?

Walsh has already stated that he has "asked around" about Zerga. The information Walsh is getting back is that Zerga is a legit arms dealer. Benedict is not in the business of arms dealing or anything outside of operating a casino, and if Zerga had been a name passed between casino owners as a guy not to do business with, he would have heard of him.

So, the fact that Benedict had not heard of Zerga, coupled with the info Walsh was getting from his contacts, led Walsh to trust his contacts and believe that Zerga was a legit arms dealer.