I saw there is a day and night Zentu for common and chibi. Does that mean there are two different options, or they change color all by themselves, depending on time of day? Thanks!

Zentu themselves do not change color with the diurnal cycle of Subeta. Whether or not you get a day version or a night version depends on what time it is when you visit the Bathhouse to adopt one. The time according to what it looks like in Shengui Guo, not Subeta Stadnard Time or your GMT adjusted real life time.
I'm not sure if the time of day matters when you chibi=fy your Zentu. Maybe they stay the same base color that they were before.
Thank you, that is interesting! They are cute. :)
you are welcome. Zentu are cute!
After I made my post I rediscoverd that NPC Som sells Zentu Elixirs in the floating market shop Five Seven Five. It looks like he has Elixirs for both Day and Night colors, so if you have the sP you don't have to wait.