Caerick's name is still Caerick, it's written on LN officially translated.
Because Mai-Mai copy Cayna's name and change it into new name, Caerick.
If you still use Kaerick, based on MAL, that's okay.
To be honest, i didnt like this route
Like, just what the f*ck they are doing
But, i like to see the ending
Because in this chapter, they look like a happy family
So, i can approve this