Professional hitmen don't actually exist. It's a 'business' that you can't possibly advertise for and has no way for the customer to assess the quality of the provider in advance. Sometimes killings do happen in exchange for money, but they don't involve someone that is a professional killer that works with the public as their primary source of income. It just doesn't exist. But there are some cases where killing does happen for money.
Sometimes two people will conspire to kill another for profit. Maybe one spouse hates another spouse. They ask a close friend or relative to kill their spouse, and they offer a portion of proceeds from life insurance as a payment for their risk and trouble. Or they're cheating on their spouse with someone else, stand to inherit all their spouses assets upon their demise, and promise to marry the person they're cheating with, thus sharing all the assets with them. In this case, it's not a stranger being hired; the killer has known the person 'hiring' them for decades.
Some killings-for-hire are gang related. A gang wants someone killed. They don't hire a random person to do it. They get one of their own members, who they've already known for many years and is a full member of the gang. In compensation for the huge risk the person is taking on to perform the deed, they offer a large sum of cash. Again, an unvetted stranger is not being hired. This person has likely already committed numerous crimes on the gang's behalf in the past. When you've already committed enough crimes on a gang's behalf to get you years in prison, a murder isn't such a stretch.
Some killings-for-hire are done at the behest of nation-states. Spycraft. The KGB or CIA hire someone in a foreign country who is already sympathetic to them to kill someone the intelligence agency wants taken out. The intelligence agency doesn't just select anyone, they go through a long vetting process just like they would any other intelligence asset. In fact, the potential assassin has likely already provided good intelligence and assistance to them for years, already risked extensive jail time or worse. If you're a US military member that's been providing intelligence to the KGB for a decade and have already participated in sabotage efforts, you're already looking at treason charges if you're caught. Offing someone for the KGB isn't such an escalation. And when a nation-state hires someone to perform a killing, they also offer the person a plausible way out. The CIA can hire someone to kill someone for them in a foreign country and hand that person a US passport along with a few million safely in a US bank account in their name. Hell, they can make sure the assassin's family has been given US citizenship and is already in the US before the deed is done. The CIA assassin can perform the killing, and as long as they can get to US or friendly territory before the foreign cops catch up with them, they'll be completely free and clear. And regardless, their family will already be set for life in the US.
These are the kinds of scenarios where killings actually do occur in exchange for money. No one hires someone to kill another that they haven't heavily vetted. If a random civilian is going to hire someone else to kill someone, they won't hire a professional assassin. They'll hire their brother or their lover. Otherwise contract killings only are done by organizations like gangs or national intelligence agencies, and they only hire people to do so that they've worked with for years and who has already committed numerous less severe crimes for them in the past.
In short, there really is no such thing as a professional assassin that serves the general public. Maybe if you are the spouse of a high-level violent gang member, you might be able to convince them to use the gang's resources to pay one of their trusted members to kill someone in exchange for cash. But if you're just a random average person? Forget it. There simply are not professional contract killers hiding in the shadows that a random civilian can hire if they have the cash. Anyone claiming to be that is simply a cop. Any person who DID try to start a career like this would be caught very quickly and have a very, very short career.
Sure. But when I say, "professional hit man" I don't mean a gangster, a mobster, or a spy. I'm referring to more of the professional hitman as seen in popular culture: https://tvtropes.org/pmwiki/pmwiki.php/Main/ProfessionalKiller
Think the trope in fiction. Someone wants someone killed. They find the shadiest person they can, like their tweaker cousin's dealer. They then ask this shady person if they can put them in touch with a contract killer. Through the grapevine, they meet with someone who is literally a professional killer-for-hire. The usual trope is some extremely well-put together gentleman; he probably wears a 3-piece suit and black leather gloves. He probably views killing as an art form. He takes professional pride in it. He's probably obsessed with expensive firearms and their various accessories, and he personally owns an arsenal big enough to take down the government of a modestly-sized city. Killing is his passion; he only charges at all because he has bills to pay like anyone else. The usual trope is to imagine someone as professional and presentable as the most formal lawyer or doctor you can imagine, except their business is killing.
While the real world version of a professional killer wouldn't be so extreme, the core should remain if they are to be a professional killer. They don't need to dress in a suit, have a private arsenal of rare expensive weapons, and speak in a British accent. But they should still meet the minimum definition of professional to count as a professional hitman. A "professional" is generally someone who offers a specific service to the public as their primary occupation. Lots of people know first aid. But only a doctor or a nurse makes medical care their actual profession. Most people can replace a light switch, but that doesn't make them a professional electrician. A professional usually sees some higher purpose or artfulness in their services and seeks to provide them to all that can afford them.
Sammy Gravano was a mobster, a terrible human being, and a ruthless killer. But he was a mobster first, and a killer second. He committed numerous other crimes on behalf of the mob, not just murder. And he didn't commit murders that weren't at the behest of the mob. You, as a random stranger, couldn't just knock on his door, hand him a bag full of cash, and get him to off someone for you. In fact, he would probably kill YOU just for trying.
Per OP's original question, Sammy Gravano does not count. There was no way for some random person back during his day to find him, hire him, and have him take someone out for them. He was a mobster, not a professional hitman-for-hire. And that is a crucial distinction.