Remember that the law is not interpreted by an inflexible computer program or robot, but by human lawyers and judges. Reasoning, intelligent people who are entirely capable of calling you on it if you try to fool them.
In this case, if your game was as engaging to play using names of nobodies, you wouldn't even need to ask this question. You could just use completely generic names with not even a coincidental link to famous people.
The reason you want to use recognizable names like "Will Smith" is that you're counting on name recognition — you can reasonably expect players will interpret this to mean the Will Smith, the famous actor, not one of the randos you found on LinkedIn. Associating this known person, and things players think & know about them, with the cards and events in your game, is a source of amusement that helps make your game more entertaining.
This is obvious to you, it's obvious to us, and it will be obvious to Will Smith's agent and legal representation. If they decide they don't approve of your use of his identity and brand and decide to take you to court, it will also be obvious to the judge presiding over the case that you're drawing benefit from unauthorized use of this famous person's identity.
In some jurisdictions you might be able to claim "fair use" or "parody," but it's important to note that this is a defense you could try to use in court, not a way to prevent being sued in the first place. You could still lose, or pay a substantial amount of time and money arguing your case even if you win.
So, the safest bet is to seek permission when you want to use anything that belongs to someone else — including their name.