The Maverick gives an interesting symmetry argument that Ockham’s maxim about not multiplying entities according to the multiplicity of terms does not support classic nominalism, namely the view that there is no singular entity, no 'universal', signified by a common term. He writes

If the Razor forbids the multiplication of categories of entity according to the multiplicity of categories of terms, then I agree, but fail to see how this supports nominalism. There are singular terms and there are general terms. Someone who maintains that only general terms, but no singular terms, enjoy extralingusitic reference would be well within the stricture laid down by the Razor as your formulate it.

I don't disagree. Clearly more is required, and we have to look to Ockham’s semantics to get classic nominalism. Ockham, in common with most 13th and 14th century philosophers of language, held that there is a relation of ‘supposition’ between terms and extra-mental objects. Thus ‘man’ supposits for Socrates, Plato, Aristotle and so on. Exactly the same relation holds between singular terms like ‘Socrates’ and the object they supposit for (in this case, Socrates). The only difference between common and singular term is that the latter are naturally suited to supposit for only one individual, whereas the former can supposit for as many as you like.

Given this, and given the Razor, classical nominalism certainly does follow. It is fruitless to posit a singular entity designated by the common term ‘man’, which Socrates, Plato, Aristotle etc., fall under in some odd way, when you can explain it in the simpler way above. A common term does not signify a singular entity. Rather, it signifies many entities.

In summary, Ockham's maxim does not on its own support classic nominalism.  We have to add his semantics as well.