You did not mention if the first name started with the Letter "E" or the last name.
Eddie Mathews is the first name to come to mind. John Edelman played one year with the Braves in 1955. If you visit the Baseball Almanac website (see Related Links) You could browse through the rosters to find the player you are looking for.
In 1955, Dave Koslo pitched in 1 game for the Milwaukee Braves. He gave up 1 hit and 1 earned run, recording no outs.
Ethan Blackaby debuted on September 6, 1962, playing for the Milwaukee Braves at County Stadium; he played his final game on October 4, 1964, playing for the Milwaukee Braves at County Stadium.
John Braun debuted on October 2, 1964, playing for the Milwaukee Braves at County Stadium; he played his final game on October 2, 1964, playing for the Milwaukee Braves at County Stadium.
Cecil Butler debuted on April 23, 1962, playing for the Milwaukee Braves at County Stadium; he played his final game on July 25, 1964, playing for the Milwaukee Braves at County Stadium.
Billy Queen debuted on April 13, 1954, playing for the Milwaukee Braves at County Stadium; he played his final game on April 25, 1954, playing for the Milwaukee Braves at County Stadium.
Charlie White debuted on April 18, 1954, playing for the Milwaukee Braves at County Stadium; he played his final game on May 29, 1955, playing for the Milwaukee Braves at County Stadium.
Mike Krsnich debuted on April 23, 1960, playing for the Milwaukee Braves at County Stadium; he played his final game on May 19, 1962, playing for the Milwaukee Braves at County Stadium.
Red Murff debuted on April 21, 1956, playing for the Milwaukee Braves at County Stadium; he played his final game on May 30, 1957, playing for the Milwaukee Braves at County Stadium.
Charlie Gorin debuted on May 29, 1954, playing for the Milwaukee Braves at County Stadium; he played his final game on April 17, 1955, playing for the Milwaukee Braves at County Stadium.
Earl Hersh debuted on September 4, 1956, playing for the Milwaukee Braves at County Stadium; he played his final game on September 22, 1956, playing for the Milwaukee Braves at County Stadium.
Dave Jolly debuted on May 9, 1953, playing for the Milwaukee Braves at County Stadium; he played his final game on September 14, 1957, playing for the Milwaukee Braves at County Stadium.
In 1956, Phil Paine pitched in 1 game for the Milwaukee Braves. He gave up 3 hits and 0 earned runs, recording no outs.