E: 05/09 - Win! A 60th anniversary Scrabble set

It became scrabble in 1948. Before that it was called Lexico.

So he set out to devise a game that was half luck, half skill. And by the end of 1931 he had developed the initial idea for the game, which he called Lexico.
They rearranged the premium squares and simplified the rules, which were overly long and reconsidered the name of the game. Then they lodged a Copyright application, which was granted on 1 December, 1948.
Soon after, came the all important name change ! After much searching, they decided upon the name Scrabble for the game and managed to register the trademark on 16 December, 1948.

So I'm guessing 1948?

Taken from the history of scabble here. http://scrabble.mattel.com/en/adults/history/page1.html