trill culture

please take a moment to imagine the Federation version of Eurovision as @swordfern and I have envisioned it, in a post-DS9 peaceful future:
-Bajor does something very soothing with hand percussion and like…. background eurythmy dancing but the lyrics are utterly heart-wrenching.
-Betazed is always a fan favorite- they really get into the pop ballads and impressive choreography, and of course aim to inspire ~feelings~
-Romulans do the super intimidating acts like that one song about Moscow Germany did one year.
-Klingons just do fucking opera every time, with intense choreography, generally involving weaponry.
-Andorians do… whatever the andorian version of death metal is. imagine andorian headbanging. with those antennae. imagine.
-the new Cardassian Republic, when it finally gains admittance, is intensely earnest and a bit disco. No one really knows how to react to this.
-Vulcan sends one person with a Vulcan lute and they play an extremely logical arrangement extremely well, with no dancers or any illogical frippery… and they repeat this each year. No one ever votes for Vulcan.

I have questions about Trill names:

Let’s take for example Ezri. Her name was Ezri Tigan. She was joined and took the name Ezri Dax.

So if you are joined, your family name is replaced with your symbiont’s name.

But what about kids? If Ezri had a kid, would they be Dax or Tigan? If it’s Dax, how do you differentiate between a joined Trill and someone who’s just a kid of a joined Trill?
If it’s Tigan, isn’t it confusing?

Either way, it’s confusing.

And while I am at it, do Trill women take the husband’s name when they get married? Even if they are joined? (I know Jadzia didn’t, but Worf technically has only one name so there was nothing to take.)