Are you sure that the Brits use
Tahnee at all, and especially as a variant of
Tawny? This seems unlikely on every level, especially the very different pronunciations of Atw and Tah in UKE, the association with tawny owls, the prevalence of
Tawny as a dog name ... and without a high-profile soap opera character named
Tahnee to kickstart a trend, I find it impossible to believe.
Though a bunch of good facts could change my mind!
If I had to guess, I'd imagine there could be a link between Tarni and the dated
Taryn.