Technically, "Britain" refers to England and Wales. "Great Britain" refers to England, Wales and Scotland.
http://www.ordnancesurvey.co.uk/blog/2011/08/whats-the-difference-between-uk-britain-and-british-isles/
http://projectbritain.com/britain/britain.htm
So, if Scotland votes yes, the name of the remainder of the country could be the United Kingdom of Britain and Northern Ireland rather than the current United Kingdom of Great Britain and Northern Ireland.