Scotland currently has a very strange currency set-up -- we're technically speaking using the pound sterling, just as England, but three "Scottish" banks have got the right to issue their own banknotes in a currency board arrangement (I put Scottish in inverted commas because the Royal Bank of Scotland is owned by UK government, the Bank of Scotland is part of the Lloyds Banking Group, and Clydesdale Bank is part of the National Bank of Australia). I don't know of any other modern countries where private banks issue bank notes in lieu of a devolved government.
After independence, there are several options available to Scotland.
As I've written before, my personal preference would be a currency board arrangement, where the National Bank of Scotland issues one Scottish crown (or pound or dollar or whatever) for each pound sterling in its vaults. In this way, it will still be very easy to do business with the rUK, but the coins and banknotes will all be issued by the NBS. The advantage of this system is that if the rUK economy collapses, the link could be broken and the Scottish crown could either be tied to the US dollar or the euro instead, or it could start to float freely, without the need to issue new notes or coins. During the independence negotiations, Scotland would of course be entitled to demand representation on the Bank of England's monetary policy board in return for maintaining the currency board (which would be to the rUK's advantage).
I think this policy would be more robust than trying to maintain the status quo exactly, where the Bank of England's notes and coins are also circulating in Scotland, because it would be much harder to change the set-up if it becomes desirable to leave the sterling zone (who knows, the euro might be looking fantastically attractive again in ten years' time).
What's important to remember here is that changing a currency takes time. No matter what the outcome is, I'd expect the status quo to continue at least two or three years after independence day (until 1st January 2019 or so), which means that the actual way forward will be decided by the independent Scottish Parliament elected in May 2016, not by the current SNP government.
The fact that Scotland can decide to implement a currency board without the approval of the Bank of England shows that the unionists' threat of the day (that there wouldn't be Scottish banknotes after independence) is absurd. Even David Blanchflower said so today ("George Osborne would be better off revisiting his misguided and failing policies for growth rather than scaremongering to the people of Scotland") and I don't think anybody has ever accused him of being a Scottish nationalist.
PS: I'd recommend following Blanchflower on Twitter. For instance, he tweeted this today:
Osborne lecturing the Scots on economics is like having a freshman who failed econ101 giving the keynote address to the American Econ Assocn
— Danny Blanchflower (@D_Blanchflower) April 22, 2013