It's instructive here to look at the etymology of "christening". It is, obviously, derived from the word Christ. Here's what the Online Etymology Dictionary has to say about christen:
c.1200, from Old English cristnian "to baptize," literally "to make Christian," from cristen "Christian". General meaning of "to name" is attested from mid-15c.
The original meaning of the word is "to make Christian", which is very much what baptism does. For instance, see the Catechism page on baptism:
Through Baptism we are freed from sin and reborn as sons of God; we become members of Christ, are incorporated into the Church and made sharers in her mission (CCC 1213)
So the original meaning of the word was very close to the meaning of "baptism".
Of course, baptism was a significant moment in the life of the child, not least because it was the first time their name would be recorded officially. (No birth registers in those days!) So the baptism/christening ceremony also had the idea of name-giving incorporated into it.
The situation became complicated by the analogous use of the words "christen" and "christening" to refer to naming ceremonies more widely, and thence to meaning "giving a name to something", as in "I christened my new car Hazel."
I'm fairly sure that the weird etymology has only happened in English (as on so many occasions in English, we have a French-derived word (baptism) and a German-derived word (christening) that mean basically the same thing), and therefore that this is restricted to the English-speaking Christian world.