What's the probability that one person will ever visit a planet that another person has landed on?

By my math, if there are a billion random visits to planets (corresponding to 1000 planet visits by 1 million players) in the 2⁶⁴ seed space, there's a 97% probability that no two visits are to the same planet, with the probability that no two people's visit sets share a planet being marginally higher (as some of the cases where two visits are to the same planet will involve two visits of the same person).

Can you see named planets from further away, or do you have to go to them to see if they have been visited before?

If your buddy named a planet "Buddy's Awesome Space Planet", can you look it up and plot a course to it, or do you have to bumble around and hope you hit it?