::It's the meaning of the source we need to keep intact, not its wording (it's usually best to avoid a avoid a sources wording). We can word this however we want so long as the meaning is the same. If it's almost universally known as the West Bank, it by definition must be generally known as the West Bank, just as a billionaire must by definition be a millionaire.  
 ::It is rather odd that the source uses both terms like that as "generally" is a much weaker term then "almost universally", but if the "generally" is not meant to take away from the "almost universally", it's totally redundant. If the "generally" is meant to somehow dampen or partly negate the meaning of "almost universally", the source is being very very unclear as to weather or not it's almost universally known as the West Bank, and we probably shouldn't rely on it for that claim (with or without the "generally and"). Either way tough, the source supports that J&S; is generally known as WB, heck that claim barely even needs a source.  
 ::There are plenty of sources out there anyway; it J&S; is almost universally known as WB (it sure seams to be: "Judea and Samaria" -wikipedia "West Bank" -wikipedia) it shouldn't be too difficult to find a source that clearly says that.