"Ockham's Razor" is a misnomer. The phrase itself was not coined until 1852 by Hamilton. The modern formulation of the princple, 'Entities should not be multiplied without necessity', is not found in exactly this wording in the medieval literature, and it seems to have originated with the Scotist Commentator, John Ponce of Cork in 1639. The medieval wording, used by both Scotus and Ockham, was 'Pluralitas non est ponenda sine necessitate' - 'plurality is not to be posited without necessity', and 'Frustra fit per plura, quod potest fieri per pauciora' - 'it is vain to make through several, that which can be made through fewer'.
Neither of these capture Ockham's nominalism - a realist may agree that entities should not be multiplied without necessity, but he (or she) will argue against the nominalist that universals re necessary. Ockham neatly formulates a principle that captures his nominalism in Summa book I, chapter 51, where he accuses 'the moderns' of two errors, and says that the root of the second error is to multiply entities according to the multiplicity of terms and to suppose that every term has something real corresponding to it. He says grumpily that this is erroneous and leads far away from the truth. ('Secunda radix est multiplicare entia secundum multitudinem terminorum, et quod quilibet terminus habet quid rei; quod tamen abusivum est et a veritate maxime abducens').
There is more about the myth of the Razor here.