Both phrases are used on both sides of the pond. Americans prefer either the plain "We have" form or the shortened "We've got" form. Britons prefer the full "We have got" more often than Americans, but the plain "We have" is increasing in usage. The most obvious difference is in negative and interrogative form usage. Look at this ngram.
Edit: Also look what some reputable sources have to say about it:
- British Council: British English and American English
Because they are generic ideas of name rather than particular instances. For a much fuller set of rules see https://forum.duolingo.com/comment/1012366/When-to-use-the-definite-article
Outside these rules, I would omit or include to match Italian and English usage.
This single sentence has appeared more times in my lessons than any other single sentence, even though I translate it, write it, etc correctly. Usually, Duo repeats the things I've gotten wrong and that's great, but it seems to be stuck on this on thing for some reason. Could it be an algo issue?
One assumes that you mean "Christian" and not "Christain". Thing is though, not everybody is a Christian so why would they have a Christian name? What they probably have is a given name and a family name, or a first name and a family name, or even several given names and a family name etc. etc. etc. etc. You can't impose a Christian name on someone who doesn't want or need one.