In order to pluralize a name, this guide says:
There are really just two rules to remember, whether you’re pluralizing a given (first) name or a surname (last name):
- If the name ends in s, sh, ch, x or z, add es.
- In every other case, add s.
Similarly, there are two fundamental no-no’s:
Never change a y to ies when pluralizing a name; and
Never, ever use apostrophes!
- The Flaherty’s live here.
- The Flaherties live here.
- The Flahertys live here.
- Sandra’s two favorite boyfriends are Charleses.
- There are seven Joneses in Stuart’s little black book—three of them Jennifers.
- The Hopkinses are coming over for dinner tonight.
So your instinct is correct -- do not use an apostrophe as that indicates possession. Your first example would be:
There are a lot of John Smiths in the world.