The first occurrence I found in in the Two TowersThe 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.’
'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.