Not quite. Thai names are actually the result of a painstaking process: a Buddhist monk must pore over various astrological charts and tables before deciding on an appropriate, auspicious (and unique) name for a family or individual. Since last names are peculiar to a family, two people with the same one are by definition related. But doesn't this mean that as time goes on, people with the same last name are going to become (on average) less and less related, as family trees expand? And since Thai surnames are sort of like hereditary titles in that they can only be carried on by a male heir, names must be going the way of the triceratops all the time. And here's where it gets really weird; doesn't this mean that eventually everyone in Thailand will have the same last name? I mean sure, it'll take millenia. I'm just saying is all.
Also: first names are likewise incredibly varied--according to Wikipedia (I mean honestly, where did you think I was getting my information from?), 35% of Thai first names are unique, which is pretty high when you think about it--one in every three people you meet has a name you've never heard before (that is, if you're Thai). And come to think of it, in three months in Thailand I can't think of any two people I've met that have the same first name, the notable exception being two different guys named Bandit (no joke). For obvious reasons, they both prefer this to their far less badass nicknames. This further explains the necessity of the nickname system; it's usually harder to remember a person's name if you've never heard it before or if it's uncommon (unless it's memorably weird, but I can't imagine what a memorably weird Thai name would be); the point is, when every name in your society is either unusual or unique, names have sort of defeated their own purpose, except for that of repelling evils spirits, curses, and other bad shit.
I have a hard enough times remembering dumb American names. Don't be alarmed if I don't remember yours.
Also, I think I just used two semicolons in a single sentence somewhere back there. I must apologize to the rolling-in-his-grave corpse of Kurt Vonnegut. Sorry!