Axel, or Akuseru, is but an anagram of the name of the man who had originally turned into a Heartless. That man's strong heart is the reason Axel exists and retains a human form despite the fact that he is a Nobody. The man's name can be one of the following: Ael, Ale, Lae, Lea, Ela, Eal, Aer, Are, Rae, Rea, Era, Ear. The reason for the 'R' is because in Japanese, the 'L' and 'R' sounds are slurred together. There is no difference in the sound of those letters to those who are Japanese. That's why although the Japanese name is Akuseru, it is translated as Axel. Therefore when finding his true name, one could substitute the 'L' for an 'R'.
So which one is it, you ask? Beats me. SE never said anything about it. They do love leaving little mysteries behind, mm?