Without wanting to sound flippant, The Mad Regent, I was thinking exactly the same thing about your way.
Yeah! Those stupid Americans! Just like this website says! Oh. Woops. Looks like you were talking about you instead.
Original question: Either works. I'd probably have neurotically included the inverted commas then decided they looked too clunky. Re: standard name for your drug... Spoiler: Opinions, dead ahead! I agree that komazol sounds more like a brand - I think because 'koma' alludes to the drug's effect, which seldom influences pharmacologic names. That doesn't necessarily make it a bad standard name though: Valium is perhaps more widely known than diazepam (maybe starting to change). It sounds like yours is a new synthetic drug, so I'd perhaps expect it to be named more chemically than 'linguistically' (e.g. methamphetamine vs heroin). If you're looking for a plausible-sounding pharmacologic name without doing a whole course in chemistry, make it a new version of an existing drug class and follow the naming convention. You needn't actually exposit on this, it'll just help the name seem real. From what I've heard about your drug, it sounds most like a dissociative anaesthetic, so perhaps make a simple random prefix for the -etamine suffix. (The real ones I know of are ketamine, tiletamine and methoxetamine.) I think anyone objecting to the chemical inaccuracy of your chosen prefix would be in the vast minority (possible exception if you add amph- to -etamine!) - but that may already apply to komazol!
Well I just flicked open Treasure Island and guess what ... Oh, woops. I think ... not. Commas don't go inside speech marks or inverted commas in the English language period.
Wait a minute. New development. It seems you're half correct. Commas go inside speech marks but outside inverted commas, which actually doesn't make any sense when I think about it. It's probably a concept that a few writers happened to incorporate unwittingly during an earlier period and it became the norm. Still, I don't agree with the concept, and though American English is bad English, it's the correct method.