So in those places, is what the priest names you at baptism your legal name? There's no birth certificate? Here in the US, your legal name is what's on the birth certificate. If the priest refuses to baptize little Zaphod Beeblebrox by that name and baptizes him as 'Francis', legally he's still Zaphod.
I saw back a few pages about saint names being required for Catholics for baptisms and it reminded me of a book I read last year where a woman in N. Ireland had picked a name she liked but her husband, MIL and SIL (who was her best friend before the marriage) went behind her back and had the child baptized Margaret Mary but the woman only ever referred to the girl by the name she'd wanted her to be called.
In Catholic Québec, years ago, it was almost mandatory to have Joseph (boys) and Mary (girls) in your name. I was the only one who didn't have Mary when I saw the registry at church. I have NO idea why, but I was kind of glad about it when I found out.
Babies were baptized soon after birth, even if the mother was not there or if it would have been dangerous to the baby (premies, etc). When one of my sisters was born, my mother wanted to name her Nancy (not real names, of course) but the priest didn't like it, so he named her Lucy-Ann. Mother didn't know for a while that Nancy was not Nancy. And no one from the family that was there went against what the priest said.
For a lot of people, the baptism name is their "real" name, not what is on the birth certificate, since a religious sacrament "trumps" governmental bureaucracy.
Actually, in Québec, until 1984 (approx.), the Church documents were the legal ones. So whatever name was on it, that was your name.
My mother had always been called Amelia but when she got her baptism certificate (for her wedding), it was Emily, with the family name having an alternate spelling rather than the one used by her father. She had to have all legal documents changed to fit her real name. As I said earlier, sometimes the mother was not present when the child was baptized. In her case, her father forgot what her mother wanted to name the baby. To add to the fun in baptized vs. use names in my family, some of my sibblings are children of Amelia, others of Emily. I don't know who the priest was in that parish, but he could not spell his way out of a paper bag.
When the civil code was revamped, the town/city hall birth certificate became the legal one. The Church document was only for religious purposes, say you want a Church wedding, etc.