A for that time remarkably comprehensive treatment on the etymology of Siam can be found in:

Yule, Henry, & Arthur Coke Burnell, 1903, Hobson-Jobson, new ed., ed. by William Crooke, London: Murray

Abstract:

the English perhaps from the Malay; earliest Potuguese had Sião (Barros, Couto), sometimes Siam (Correa), also Sião "Siam, the country" beside as Siames "the Siamese, the people" (Barros, Pinto); van Linschoten, probably basing on a Portuguese source, had Sian. Term is "identical" with Shan and Chinese Sien(-lo), See also pp. 821-823 under Shan

for Chinese Sienlo (Pinyin: xinluó)

Pulleyblank, Edwin G., 1991, Lexicon of Reconstructed Pronunciation in Early Middle Chinese, Late Middle Chinese, and Early Mandarin, Vancouver: Univ. of British Columbia Press

xin

Beside Shan, there still are Assam and Ahom, which are apparently cognate to Siam as well (I can't remember what reference I got the Ahom alignement from, perhaps Grierson's Linguistic Survey?).

Cognates in Chinese, Vietnamese (perhaps loan from Chinese?), Khmer, Mon, Burmese, Malay, Javanese, all point to an original sya:m or sia:m (":" indicates long vowel) rather than the present Thai Saya:m. I'm therefore inclined to place the derivation of Common European Siam from "English-spelled" Saya:m in the vincinity of folk etymology.

Also from the realm of folk etymology is probably the derivation from Thai saya:m "reddish brown" in allusion to the skin-colour of the Thais (which many other peoples in SE Asia would hardly see as a feature distinguishing Thais from themselves, least of all such favourite enemies of the past as the Burmese and Malays).

Waruno.