Thanks all, I'll draft a more considered response shortly, and apologies if this has taken the thread away from Sean's original list...
The vast majority of golfers from Nottinghamshire will call it Hollinwell.
I had always assumed this name came about when the club moved from it's original Bulwell (central Nottingham) location to the present one. So although still Notts Golf Club (I assume short for Nottingham rather than Nottinghamshire so like Notts Forest or Notts County football clubs) they were playing at a different venue and needed to differentiate themselves from the club that formed at their old site...
As for marketing I think Phil Stain, the course managers twitter is excellent;
https://twitter.com/phil19672611
Tom,
Firstly, and perhaps most importantly, its NOTTINGHAM Forest and NOTTS County. Mentions of Notts Forest will generally get you lynched around here!
As for the clubs name, originally founded in 1887 as the Nottingham Golf Club, in 1893 the club would change its name to the Notts Golf Club. Notts is the acknowledged shortened version of Nottinghamshire and indeed for quite a few years after the name change Nottinghamshire Golf Club was often used in correspondence and appears on medals, buttons and other memorabilia.
On moving to a new course north of the city in 1901, the course adopted the name Hollinwell, after the holy well at one time used by the monks of nearby Newstead Abbey. The club retains the formal name Notts Golf Club (Hollinwell) referencing both the club and the course.
And yes Phil's twitter is excellent. I especially like his recent man made Kingfisher nest on one of our ponds!
Cheers,
James