We don't have to change any vocabulary. Noon and midnight happen at different times in different places and that would be fine. We know it's fine, because that's how it currently is in China.

Most servers run on UTC under the hood, and a lot of big organizations have experience already in terms of doing all timekeeping calculations in UTC. It may seem weird, but works pretty well in the long run -- and not having to deal with corner cases like DST or geographical ambiguities around time is extremely valuable.

Have you ever thought about what it's like to live near the edge of a timezone? In a city where half the city uses one time and half uses the other?