It has to be a good idea to think of a better way of refering to what has variously been called the Tridentine rite, the Traditional Rite, the Usus Antiquior, and the Extraordinary Form. But I'm not convinced that Cardinal Castrillon Hoyos has hit a winner with 'the Gregorian Rite'. Firstly: Summorum Ponyificum cleverly made clear that the EF is not a separate rite; if it had been, there would have been enormous canonical problems about its status and the acquiring of permission to say it. By emphasising that there is only one Roman Rite but that there are two forms of it, the Holy Father sidestepped that.
But also, historically, why 'Gregorian'? The elements of the Ordo Missae as they left the revising hand of Pope S Gregory I remain in the post-conciliar rite - at least in that usage of it which sticks to the Canon Romanus - with few changes I can think of off-hand: in the Institution Narrative and in the Libera nos. The preparation at the foot of the Altar; the private prayers at the Offertory and before communion, are post -Gregorian. The Sarum Rite, for example, had quite different texts.
There must be a better term. Otherwise, calling it the Extraordinary Form might have one apologetic advantage: Bishops could be asked to oppose the Extraordinary Form no more than they oppose Extraordinary Eucharistic Ministers.