Long associated with the Churchill family and common in the West Indies, the distinguished Winston has tended to be neglected here. The exception was during the World War II period, when Winston Churchill was a towering figure and his name reached Number 234. It's now enjoying something of a renaissance, reaching Number 538 on the US Top 1000, a level of popularity not seen since the 1950s.
Winston Smith is the main character in George Orwell's 1984, is a presence in Pulp Fiction, is the name of a character in the best-selling book and film How Stella Got Her Groove Back, and was the middle name of both John Lennon and John Howard, long-serving Australian Prime Minister. Billie Piper and Laurence Fox named their son Winston in 2008.
With the current trend towards using hero names, we can see this upstanding Anglo-Saxon example making a return.
The nickname Winnie came into the public consciousness with the Winnie-the-Pooh books, but is now almost exclusively feminine--though you can shorten it further to the winning Win.
Minor irritant: Connection to the cigarette brand.