What is the name given to a score of 3 under par for one hole?

Depending on where you live and play the answer will be either an Albatross or Double Eagle.

More about a score of 3 under par

Albatross was the original British term used. The exact origin is unclear but the first written reference dates back to a newspaper article about a local golf match between Durham and West Hartlepool, captained by their respective Mayors in 1929.
In America Double Eagle become the common term after being reported as such in the press after Gene Sarazen holed out for 2 on Augusta National’s 15 ^th hole in the 1935 Masters.
Logically the term Double Eagle actually makes no sense. An eagle is 2 under par which means that a double eagle should be 4 under par.
The first 3 under par score reported in the press was in South Africa in 1931 where E.E. Wooler scored a hole in one on the 271 yard par 4 18^th.
According to former Golf World writer, Bill Fields, the odds of scoring an albatross / double eagle is 6 million to 1.
There are lots of video clips of great golf shots going in the hole for an albatross / double eagle. We chose this one to Fire up your Golfing Soul because we love the tracking of the ball as it crosses the green towards the cup on 2 at Augusta National.

It's an albatross," Padraig Harrington once said, incredulous that anyone would dare call it anything else. "There's no such thing in life as a double eagle. Is there? Two eagles side by side are two eagles, not a double eagle. You don't refer to animals ... 'Oh, I just saw a double elephant over there.' There's no doubting what it is. It's an albatross."