The phrase Christian name is best replaced these days by forename, which is more accurate. A forename is that part of the name which we in the UK traditionally put first, before the surname. Some writers prefer the term 'given name'; but in some cultures all names are given, and none are necessarily 'family names' or 'surnames' in the same sense as used in traditional British culture. The order in which names are written also varies between cultures; but in conversational use in the UK, there is a recognised order. All writers should be aware of that order, and vary from it only when deliberately choosing to do so.
Traditionally the forename was a name given in a Christian naming ceremony carried out in a church shortly after the baby was born. (The ceremony is called baptism or christening; the verbs are 'to baptise' and 'to christen'.) Many people in Britain today are not Christians: many are members of other faiths, or of none. It can be insulting to suggest to a confirmed atheist or devout Muslim that she has a name given to her by virtue of Jesus, called 'the Christ' by Christians. You are advised to use the neutral word forename.
(If you are writing History, or a number of other specialised subjects, there may be an excuse for using the term Christian name in the UK in the 21st century; but these occasions are rare for most students.)