The sport of ice hockey uses the term 'hat trick'.
A hat trick in any sport is three goals.
When a player scores three goals in a game.
No it would not.
A hat trick is 3 goals in a hockey game. The tradition is that fan's literally throw hats on the ice after a player scores his 3rd goal. Frequently the term is expanded and used colloquially to mean 3 of anything in other sports as well. For example, if an outfielder in baseball has 2 errors and has trouble with a fly ball the announcer might jokingly say "I guess he is going for the hat trick".
Because a double hat trick is really just 6 goals, then technically, yes. But there is not actually a double hat trick, it is just a made up term.
The term "hat trick" was first used in 1858 to describe the accomplishment of H. H. Stephenson; taking three wickets in three consecutive balls. A collection was made, as per tradition for an outstanding achievement by a sportsman, and a hat bought with the proceeds was presented to him. While not the first to do this, it is the first recorded instance of such an performance being called a hat trick.
Hat Trick started as a cricket term used to describe a bowler who took three consecutive wickets. The term is now used in other games and is often applied in soccer to a player who scores three goals in one match.
In sport "3 in a row" is generally described as a hat trick.
Hat Trick Productions was created in 1986.