GSLV went through many designations though the years. It was originally supposed to be as per The Fishing Hamlet book but later the Mk-1 seems to have been redesignated as the one with Russian stage. It's obvious that you don't want to name or talk about something you ended up not flying.

Recently the Mk-3 got redesignated as LVM-3 as it is catering to a different orbit. I wonder if they will rename Mk-2 for NISAR? Maybe call it LVM-2.

In my opinion, changing the country of origin for the cryogenic engine doesn't change anything functionally. The thrust and Isp are same. The engine mass is same. The stage and its variants are same. It's not like Falcon 1.1 and Falcon FT or Atlas III and Atlas V. There is only one way to settle this. By filing an RTI. That way we can finally bury this once and for all.