It's called 'The Bonnie Game' after my cousin Bonita that introduced me to it... I've never known a more official name for it
Four players at a bare minimum, but ideally about six to ten.
Some scraps of paper and writing implements
A bowl to put the bits of paper in
Some mechanism with which to time thirty-second intervals (e.g. a wristwatch with a second-hand, or an egg-timer if you want to be really flash).
Each team tries to amass the greatest amount of points by the end of the game.
In the interests of fairness it's important to do this before you divide into teams
Each player writes, in secret, three names on three scraps of paper. The only requirement for a name is that it must be someone that a majority of players are likely to heard of. For example, Florence Nightingale, Jimmy Stewart, Groucho Marx, Garfield, or just your friend Bob. The scraps are folded and placed together in the bowl.
Players are divided into two teams. Teams take it in turns to play. On a team's turn, they have one active player - within the team, players should take turns to be the active player.
When one team is playing, a member of the other team should act as timekeeper.
Decide which team is to go first. The timekeeper, from the other team, calls 'Go!' and begins to time thirty seconds.
The active player takes a scrap from the bowl and unfolds it to read the name on the paper. They must try to communicate the name on the paper to their teammates without saying any part of the name. (This will be familiar to viewers of the UK gameshow They Think It's All Over).
For example, if the name was Maddona, the player might say "Female, American, pop singer, sang Like a Virgin" and probably at about that point, someone on their team would call "Madonna!" If not, the active player can keep talking as long as they like.
It should go without saying that giving away letters of the name (e.g. "It starts with M!") is Right Out.
Once the player's team has guessed the name, the player puts adds the scrap of paper to their team's scoring pile. (They don't return it to the bowl!). The player can then take another scrap and try to communicate the name.
This continues until the timekeeper calls "Time!" to announce that the thirty seconds is up. The player returns to the bowl the scrap that they are working on when "Time" is called.
Note that if the player unfolds a scrap of paper and sees a name they don't recognise, they can refold it and return it to the bowl, and get another one. Of course, this wastes valuable seconds.
The bowl then passes to the other team and the process is repeated. Eventually, the bowl will be empty, and both teams will have a collection of the scraps containing the names they successfully guessed.
Each team scores one point per name guessed. The names are then refolded and returned to the bowl for the second round.
Round 2 is almost identical to Round 1, with one crucial difference. The active player may only use one word to describe the name they are holding. Fortunately, since you've just played Round 1, you've already heard all the names that are in the bowl, so it's not nearly as hard as it sounds.
For example, a player trying to communicate Garfield in one word could say "Cat." More inventively, or if there were a great many cat names in the bowl, they could say "Odie", and hope that someone makes the link. If a player accidentally says two words (easier than you'd think), they must return the name to the bowl. Note that acronyms count as more than one word! (E.g., you can't say 'M.P.', because it stands for Member of Parliament, which is three words.)
If, after pronouncing their carefully chosen single word, a player is merely subjected to blank faces, it's up to them how long they wait for their team-mates to guess correctly before they give up and return the name to the bowl.
Retroactive guesses are not allowed! If the active player gives up and returns the name to the bowl, it is too late for someone to figure out the name and call it.
As with Round 1, play continues until the bowl is empty. Players score a point for each name and return them to the bowl for Round 3.
This time, it's mime. No speaking, no sound effects, just your very best physical impression of Groucho Marx, or whomever. By this time you've heard all the names twice, so even the worst mime should eventually be guessed.
At the end of Round 3, it's all over. Total up the scores, congratulate the winners, commiserate with the losers and explain to your team-mates exactly how that was supposed to be Florence Nightingale.
Round 4 - communicate the names using only telepathy.
Obviously there are plenty of variations you can make with the number of names you enter, time allowed, and so on. (Thirty seconds does seem to be ideal though - it's longer than you might think).