In the movies Sam is often referred to as Samwise, and there is a chapter in the book called 'The Choices of Master Samwise' but I've never come across anyone calling him 'Samwise' throughout the story.
Do any of the characters refer to Sam Gamgee as 'Samwise' in the book?
Yes, "Samwise" is used in a number of places. It's mainly used in formal manner to emphasise something (by Frodo), or by suitably formal people who would use one's first name - Faramir and his men.
Some examples:
"I don't know how long we shall take to – to finish," said Frodo. "We were miserably delayed in the hills. But Samwise Gamgee, my dear hobbit – indeed, Sam my dearest hobbit, friend of friends – I do not think we need give thought to what comes after that."
And when meeting with Faramir and his men:
"Frodo son of Drogo is my name, and with me is Samwise son of Hamfast, a worthy hobbit in my service."
...
Mablung laughed. "I do not think the Captain will leave you here, Master Samwise," he said. "But you shall see."
...
"Now you, Frodo and Samwise, will come with me and my guards," said Faramir.
There are many other examples while Frodo and Sam are with Faramir in Ithilien.
The first occurrence I found in in The Two Towers chapter 2:
'I don’t know how long we shall take to – to finish,’ said Frodo. ‘We were miserably delayed in the hills. But Samwise Gamgee, my dear hobbit – indeed, Sam my dearest hobbit, friend of friends – I do not think we need give thought to what comes after that. To do the job as you put it – what hope is there that we ever shall? And if we do, who knows what will come of that? If the One goes into the Fire, and we are at hand? I ask you, Sam, are we ever likely to need bread again? I think not. If we can nurse our limbs to bring us to Mount Doom, that is all we can do. More than I can, I begin to feel.’
Sam isn't called "Samwise" very often, but it occurs regularly through the second and third books, but oddly not at all in the first book.
Yes, for One you are forgetting the famous 'Samwise the brave' which is in the book as 'Samwise the stouthearted' and numerous other occurrences.
