It’s also a personal choice of Bethesda not to rename their engine. Many other studios do this same thing and reuse engines, but they often rename them after significant rewrites. Bethesda just doesn’t do that.
Also they aren’t worried about how the game will be released. Their games have legs. So a 60fps version will eventually come out. Then they’ll release it 5 more times.
But they did? For Oblivion it was Gamebryo, for Skyrim it was the Creation Engine
https://en.m.wikipedia.org/wiki/Creation_Engine
The Creation Engine is a 3D video game engine created by Bethesda Game Studios based on the Gamebryo engine.