I've checked Wiki...

"Perhaps it is an extension of the name of one of the native trees, mui. Some people believe that the word "samui" derives from the Malay word "saboey", or "safe haven", although there appears to be no credible corroboration of this"

 

However, other day I was told by a member of a native Surat/Samui family that locally Sa-Mui means wet or rainy place ..... this clearly makes sense but I can't find any language or dialect translation to confirm this.....anybody throw light on the matter?

Khomchadluek narrows it down to three options in an article from 2009:
1) It comes from and is a contraction of the Sanskit/Tamil word สมวย, meaning sea weather. This may be where your 'wet or rainy place' comes in.
2) It comes from the name of the tree known locally in Southern parts of Thailand as ต้นหมุย ( full name ต้นสมุย).
3) It originates from early Hainanese traders to Samui, 100--150 years ago. In Hainanese Chinese,  เซ่าบ่วย means first island, barrier or door and it got its name as it was their first port of call as it were to Thailand when trading. It later changed over time to สมุย.
There are probably other explanations eg from the Malay word "saboey", or "safe haven" after it was settled by fishermen from the Malay Peninsula centuries ago.
You pays your money, you takes your choice.
http://www.komchadluek.net/news/local/25143