Namba forcing is the first instance of a forcing which singularizes ω2 while preserving ω1. Several versions of Namba forcing exist which have shown to not be equivalent under CH by Magidor-Shelah as well as Jensen. 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(ωV2)=ω 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.