I don't know that renaming the input to PC has any effect on input lag. I'd doubt it. But there is a definite difference in game mode. Unfortunately there isn't an easier way to enable / disable it. I have a 3007WFP-HC on my test bench and jumping back and fourth I haven't noticed a major difference in input lag between the two. At least not in game mode.
I am still coming from ROG Swifts so they both feel a little "slow" to me.
After renaming HDMI 1 to "PC" and setting the device type to PC as well, I can no longer enable game mode.