There are many different variations of Namba forcing, for example the standard formulation Nm consisting of $\omega_2$-perfect trees and the variation Nm' of those $\omega_2$-perfect tree which split everywhere above their stem. Magidor-Shelah have shown, assuming CH, that Nm is essentially different from Nm' Jensen proved an even stronger theorem in which he differentiates Nm and Nm' further from the variant of Nm' consisting of those trees in Nm' all of whose nodes above the stem have stationarily many immediate successors. Jensen also assumed CH.
We generalize these theorems by removing the CH assumption and taking into account many more variations of Namba forcing. Further, we show that all ``natural" variations of Namba forcing generate extensions which are minimal conditioned on $\cof(\omega_2^V)=\omega$ and moreover, we analyze exactly which and how many other sequences in such an extension are generic for a variation of Namba forcing. Further, we show that no Mathias-style characterization for variants of Namba forcing are possible except for Priky-style forcings. This answers a question of Gunter Fuchs.