Fatty Lumpkin was noted as being fatter than the ponies of Frodo and his companions, and this is doubtless the source of his name. The -kin ending is a diminutive, so the pony's full name means something like 'fat little lump'. This choice of name may have been influenced by the word 'bumpkin' (the origins of which are obscure, but the word may have originally meant 'little barrel'). Indeed Tom Bombadil gave the name 'Bumpkin' to one of the Hobbits' ponies, so providing him with a convenient rhyme for Fatty Lumpkin's name.