Why on earth do you think they wouldn't?
This isn't some sort of separatist movement which has taken an area of land and declared themselves a country, this is a legal process of undoing a treaty from 300 years ago...
Also many maps will likely already have England, Scotland and Wales indicated on the landmass which makes up Britain so it isn't like it's a massive undertaking.I'm just stating what I was taught in high school '96-'00, which I suppose it could have changed in 14 years, but when I was in school our government teacher told us that the nation (US in my case) had to acknowledge the independence before they would bother updating their maps and just because the nation (in this case UK) acknowledges it doesn't mean other nations will. The US likely won't update our maps until we have communication between us and Scotland (if it gets its independence).
EDIT: Looks like it will be a no, according to the link dsm1891 posted.
While high by most voting standards, 84% turnout on something like this feels kind of depressing.
As for the maps thing, you're right, but most everyone is on good terms with scotland, and would recognize their status as an independent nation pretty much immediately. This isn't like China and Taiwan or something.