In Season 2, we meet L's successors, "M" (Mellow) and "N" (Near). Seeing how they are his successors and were all raised in the same institute, L must also stand for something.
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2Related: anime.stackexchange.com/q/19420, anime.stackexchange.com/q/12904 – senshin♦ May 12 '16 at 23:24
In the manga and the anime doesn't reveal what L stands for, but in a especial edition called "Death Note 13: How to Read", reveal that L real name is
L Lawliet or in japanese, Eru Rõraito.
Reference: http://deathnote.wikia.com/wiki/Death_Note_13:_How_to_Read