Looking at the Area 51 commitment page, I realized that some of the questions that were originally suggested there never got asked here, so I thought I'd add some of them. To expand on this question, was this transition a result of some military action, political influence, or external influences from other countires?
Thailand converted over from Siam after the revolution of 1932, where the nation's military staged a coup against the monarchy and established a constitutional-style monarchy (although it ended up being decades of military rule). While there was a brief return to using the Siam moniker after WWII, the new name for the country stuck.
A more detailed version of the Revolution of 1932 can be found here on Wikipedia.
To clarify the above answer: Siam ceased to be an absolute monarchy in 1932 and adopted a constitution in a (relatively) bloodless coup. The immediate effect of the coup was to give extraordinary amounts of power to the aristocracy and ranking officers, leading the country to be dominated by the military for the next 60 years.
The country was renamed from 'Siam' to 'Thailand' in 1948, partly to appear more 'modernized', and partly because 'Siam' in the west is associated as a Japanese ally.
Sources: I'm Thai and this is the history we were taught.