If I use a prepaid gift card and fake name and billing address would this be illegal?
Generally speaking, no. Since you left the type of product and its T&C unspecified, assessing whether or why your scenario would trigger an exception would require us to speculate.
The purchase/transaction constitutes a contract. The supplier delivers its product in exchange for a payment. The form of actual payment (rather than a promise of payment) is mostly irrelevant except maybe for (1) implementation of return policies, and/or (2) a cognizable need for accuracy in the registration of the product.
Suppose a person visits a store and pays with cash. From a legal standpoint, it is generally irrelevant whether that person identifies himself as someone else; and the supplier is interested only in getting compensated for his product. The exceptions to this depend mainly on whether the commerce of a product is subject to legal constraints (such as the prohibition of underage drinking), although your question nowhere suggests that that is the case.
The only difference between the preceding scenario and the one you describe is the venue for that transaction and hence the form of payment. The fact that you would do the transaction with a prepaid gift card gives the supplier the same assurance that he is getting compensated as effectively as if you paid with cash. Hence the form of payment is irrelevant to the supplier insofar as he is getting the compensation he required for the delivery of his product.
Therefore, any false details of an irrelevant item such as the form of payment in this context are generally inconsequential from a legal standpoint.