Mine sz GSX1300R and I’ve never thought of it as a Gixxer eitherI don't have a GSX or R on my bike...don't need to advertise....and the insurance companies here don't refer to it as a GSXR, nor does Suzuki.
I love my bike but......it is just a bike no more, no less, I don't worship it, I ride it.
In all honesty, if Suzuki called it a Katana, I'd still ride it with honor befitting the name. I will never knock the name Katana, I owned a pop up version for almost 30 yrs.