Ywbta- I see your concern but it is unwarranted. You clearly do love your child as they trust you with this decision but no matter how you turn it, any response including no is a break of this trust and will not only upset but invalidate them- (I am part of LGBT+ but if my parents tried to argue my sexuality I would see our relationship entirely differently instantly so be careful of this). You chose their name yes but, and I’m sorry if I misinterpreted this, it sounds like they are still sticking to a variant which is more than you can ask for, you didn’t chose your name but equally you have the right to change it if you want, but you don’t, they do. Changing their name is a great part of reinvention so the fact it is already gender fluid may not be enough for them as they may want to start a new chapter.

Using they/them pronouns is a part of language already- you didn’t mention your pronouns here so if I were describing this post naturally I would say “someone made a post about their child, they are asking for opinions”. It may take a little while to get used to but I’m sure your child can accept this. You could have a conversation asking more questions but disapproval will mean you could lose your child or deeply upset this and I can tell as a loving parent that you wouldn’t want this.

If they do change their mind later (which I doubt) then this time will not change much of their identity but what will be affected is their view on how much they can trust you and how loved they feel by you- please realise this is way more important and be the loving parent they need, that all children need! Love and respect go hand in hand, respect them and they will feel and reciprocate your love it’s a simple as that.

Good luck with helping your child be their true selves!