Question

How can a female child have a different last name than birth parents,

Comments

By the way the link to the marriage doesn’t work for me.

Answer 1

I usually see it happen when a woman has more than one husband.  Sometimes the name of her first husband is mistaken for her maiden name.

Answer 2

She might be adopted or a cousin taken in by a relative.

Comments

Or a child raised by grandparents.

Answer 3

I mean, I did/do.

It's basically due to patronymics but there's a bit more detail that would be distracting.