Birdie and Bogey
As stated in a Street Fighter I development interview in Gamest Issue #16 (thanks to vasili10 for the info), Birdie and Eagle were originally planned to be named Birdie and Bogey. Both characters are from England and share the same stage. "Birdie" and "Bogey" are golf terms and were chosen as typical English words for the two English fighters. After much laughter Bogey was renamed Eagle, which is another golf term.
Ironically Birdie's dark skinned remake from the SFZ series has a move where he seems to shout "Boogie!" but it's most likely "Bull Heat".
(Birdie and Eagle aka Bogey from SFI)
In common with others, the Historical Dictionary of Golfing Terms (1993) believes that "Birdie", meaning a score of one stroke under Par on a given hole comes from the 19th century American slang term "bird", meaning anything excellent.
"Bogey" was the first stroke system, developed in England at the end of the 19th Century. The full history is given in Robert Browning's History of Golf 1955.
"Eagle", a score of two under par for a given hole, was clearly the extension of the theme of birds for good scores from a "Birdie" (see above). It would be natural for American golfers to think of the Eagle, which is their national symbol. A score of two under Par is, in some ways, a 'big birdie' and an Eagle is a big bird. Ab Smith said that his group referred to two under as an 'eagle'.