How many people do you need to know before it's likely that two have the same full name?
The answer is going to depend critically on the pool of people you are sampling from, and whether you count people in multiple generations as Sr., Jr. as "same name". Similarly, middle initials or middle names will be distinguishing marks. What I'm after is less about collisions within a family and more about two John Jones in your addressbook, otherwise completely unrelated.
I suspect that the number is in the low thousands, just from personal experience.
How would you approach this problem?