It was published in The Atlantic as "The Negro is Your Brother," published in some places as "Letter From a Birmingham Jail" or "Letter From Birmingham City Jail," and sometimes known as "that famous letter MLK wrote that one time." But "Letter from Birmingham Jail" is the title that seems to have stuck the most, so that's the one we're using.

These slight variations are probably due to the irregular publishing history of the text and the several versions that were released over the years. It was sometimes published in full, sometimes in abbreviated form. Dr. King even published a "polished" version in his book, Why We Can't Wait, in 1964 (source).

P.S. Dr. King actually wrote the letter from inside the Birmingham Jail. He loves metaphors, but this ain't one. It's an even more appropriate title because Dr. King was intentionally breaking racist laws to call attention to them, fully expecting to be thrown into jail.