Obviously you would want to reword the ESB and ROTJ crawls a little, but you would also need to edit the ROTJ rebel briefing scene.
Mon Mothma refers to it as “the Emperor’s new battle station”. Luckily, it is in a wide shot, so you should be able to just cut out “new”. Also, Mon Mothma and Ackbar refer to it as “this Death Star” a few times, and I would recommend to trim it so it sounds like “the Death Star”, but I guess that might not be 100% necessary.
Also, if you really wanted to, you could possibly change the “Death Star plans presentation” in the ANH Rebel Briefing to make it seem like the plan involves overloading a single reactor within the Death Star rather than the main reactor, since Rogue One seems to indicate that the Death Star has multiple reactors. It could help explain why it didn’t blow up completely, but enough to severely damage it.
EDIT: Maybe the end of the animation could be altered to show that the Death Star internally has a multiple reactors, set up like spikes on a wheel, and instead of the proton torpedo going to the “center axle”, the center of the Death Star, it can go to one of the spokes where the explosion animation can happen. This isn’t necessary but it could be one option to help differentiate the ANH attack to the ROTJ attack.