'D'P is being an arse.
I would tell him that you both need to discuss this sensibly, as adults and take both your preferred names off the table and find something else you can both live with.
If he refuses I would be giving baby your surname (or both your surnames at least) and choosing the first name.
Of names you have liked Cassius, Mathias and Elias/Elyas are lovely.
As you are not married you can register baby alone and choose the full name.
Alexander and Christopher are nice names, but you don't like them, and I don't think they go very well with Amayah anyway.
Something like Cassius, Mathias and Elias, and names like Asher and Idris go better with Amayah.
I think Alexander known as Xander would work, but he doesn't get to bully you into a name, especially not when you've just given birth. How dare he spoil this time for you!
I also find it concerning that he is so adamant his son should have a Christian name when he seemingly didn't have this criteria for his daughter.
How did you agree on Amyah OP? Did you suggest it and he ok it? Were you both broadly on the same page girls names wise?