As phrased your question is a little ambiguous as it's never really possible to know why one trend catches on while another fades away. So here are some facts along with a little speculation.

Replacing one's birth, or slave name, with an X was a tradition within the Nation of Islam. The Nation of Islam was a religious sect headed by a man named Elijah Muhammad (born Elijah Poole) at the time Malcolm joined. Though they followed the Koran and maintained many of the trappings of Islam, it was disavowed by most orthodox Muslims at the time Malcolm was a part of it. Less widely known is that many Nation of Islam members also took the name "Shabazz". Malcolm, for instance, married Betty Shabazz and also used the name Malik al-Shabazz at other times in his life. This is all to say "X" names were common in the Nation of Islam as it was expected of anyone who truly believed Elijah Muhammad was Allah's final messenger.

Without a doubt, it was Malcolm himself who popularized the "X". His brief but hugely important time in the national media spotlight in the early 1960s diffused Nation of Islam teaching and ideology much further than it had ever gone before. Most estimates put membership in the Nation of Islam in the early to mid-50s in the hundreds. By the early 1960s there were tens of thousands of followers (estimates vary widely but a Malcolm biographer puts the number at 75,000 by this time). Out of 22 million African-Americans in the country then that number is pretty small. Malcolm's many media appearances reached millions more...all over the world really. He was routinely brought on television and radio to be the voice of militant black America - usually to debate non-violent civil rights activists. This is a big part of Malcolm's media profile but he had many more dimensions to his personality and intellect than just anger and outrage.

As for why this trend didn't catch on (this is the speculative part) the simplest theory is because the Nation of Islam never commanded a broad following in the African-American community...even at its height. Its media profile far outstripped its actual following particularly when Malcolm was alive. When Malcolm was assassinated the media spotlight that had shown on the Nation of Islam dimmed. To make matters worse the murder was carried out by Nation of Islam members as Malcolm had, by 1964, split with the Nation of Islam and denounced Elijah Muhammad as a liar and hypocrite. Undoubtedly, this further reduced the appeal of the Nation of Islam to the vast majority of African-Americans and with it naming conventions like the "X". Most African-Americans were Christians. They may have been intrigued by people like Malcolm X but that didn't mean they wanted to join the Nation of Islam (or take a name that made them look like they were members).

Interestingly, the "X" has become something of a media phenomena - a symbol of Malcolm's ideas and personality more than the simple religious tradition it started off as.

As for sources, I have spent several months researching Malcolm for my work. I've watched hours and hours of his media appearances and read quite a lot. Here are a few options for further reading from which most of this answer was drawn:

Malcolm X: A Life of Reinvention - Manning Marable

The Autobiography of Malcolm X: As Told to Alex Haley

By Any Means Necessary - Malcolm X: Real, Not Reinvented

I am not a professional historian so I welcome an actual scholar's opinion on this subject. Also, please do yourself a favor and read further about Malcolm X. He is a fascinating person and well worth the time.