0 names. Blank lines are ignored.
How the random name picker chooses
Each line you paste is one entry. To pick three names, the list is shuffled and the first three are taken, which is the same as drawing three slips from a hat without putting any back. No entry can come up twice in one pick, and every entry has the same chance of being among the three: three in thirty for a class of thirty.
The order of the picked names is random as well, so if you need a first, second and third speaker, read them off in the order shown. A name written on two lines counts as two entries and has double the chance. The page points out repeated names when it finds them, because in a class list that is more often a paste that happened twice than two students with the same name.
A name picker for classrooms: why remove picked names
If the full list stays in place for every pick, the same student can be called on three times in one lesson while someone else is never asked at all. Each pick is still even, so in a narrow sense that is fair. It does not feel fair to the class, though, and it is rarely what a teacher means by taking turns.
With Remove picked names turned on, each name leaves the list the moment it is picked and moves to a separate list underneath. Everyone is called once before anyone is called twice, and as the list shrinks the remaining names become more likely, one in twenty-nine after the first pick from thirty, then one in twenty-eight. When the list runs out, Put them back restores everyone for the next round. The list itself is not saved anywhere, so for a class you call on every week, keep the names in a document and paste them in.
When a pick has to stand up later
Choosing who reads next is one thing. Choosing who wins a prize is another, because the people who did not win may reasonably ask to see how it was done, and a pick made on this page leaves nothing to show them. For that, Winner Picker draws from a list you upload and publishes the winners on a permanent link, with the full entry list attached so anyone can see the pool the names came from.
Where the randomness comes from
This tool runs entirely in your browser, using its built in cryptographic random number generator. Nothing you type is sent to us, nothing is stored, and each result is thrown away the moment you leave the page. Numbers are drawn without the rounding bias that the usual shortcut introduces, so every outcome is as likely as every other.
Because nothing is recorded, a result here proves nothing to anyone afterwards. If you need a drawing that other people have to accept, for a prize, a campaign or an audit, use Winner Picker, which publishes each result on a permanent link with a signed record anyone can check.