You say you're not religious. Let's start there:
1) Jesus Christ was religious; he was Jewish. He believed in the ten commandments and he adhered to Jewish rituals. Christians do the same: they believe in and adhere to the ten commandments and they follow religious rituals. If you do none of the above, then you are not a follower of Christ.
2) Followers of Christ believe in a higher power: God. God, to the Christian, is a three-part God: the Father, the Son, And the Holy Ghost. If you do not believe in God, then you are not a follower of Christ.
3) Most followers of Christ believe in an afterlife. They believe that when you die, if you have lived a good life and have taken Jesus as your saviour, then you will go to heaven where you will be one with Christ. If you do not believe in an afterlife and rather believe that when it's over you just cease to exist, then you are not a follower of Christ.
The hardest part for you may be that, although you were given a name the means "follower of Christ," you don't believe in anything that the followers of Christ believe. So be it.
One last thing, though: don't worry that you don't match the meaning of your name. Just act according to this rule, and things should work out for you: Don't do anything to anyone else that you wouldn't want done to you.
This task seems to be something that you have to do yourself. You know who you are and who you aren't. Still, I'll try throwing out a couple of ideas that might get you started on your second and third reasons:
1. Why were you given that name? Did the person(s) naming you have a particular reason other than the common meaning of the word? Maybe the reason that you were named what you are named (Christine? Christian?) has little or nothing to do with religion.
2. Are you not much of a follower? Idea #1 is better, but if you need, maybe you could pursue this idea, too.
It would be very nice if names of people always gave some description of some actual trait or quality of the person bearing the name. But frequently that is not the case. As a matter of fact the purpose of name is no intended to represent the quality of the person, but just to identify the person, and distinguish him or her from others bearing different names.
If I was in your place I would not bother very much about my name not being in line with some of my basic characteristics. As a matter of fact my name represents name of an incarnation of a supreme being as per Hindu philosophy, that is someone much more important than God as generally understood by people. It would amount to gross arrogance and impudence on my part to think even for second that any qualities in me justify that name. And my case is very similar to that of millions of people in India. All thees people just think their name as an identification tag, without bothering about the original meanings of the names used.
I guess your name might be Christian. A name is often given to a child for more than one reason. For example, names are trendy and stylish just like clothing. Right now the name Emma is one of the most popular female name.
Your name may also have been chosen because your parents knew someone they liked with the same name. Naming a person after a favored person or a family member is common. I have four granddaughters and they all have my Mmiddle name as their middle name. My grandsons all have their grandfather's middle name as their ,middle name. (Believe me, we did not ask that to happen to those poor kids. However, we are honored.)
Your name may not fit you because you just don't like it. I have known people who have changed their names when they grew older because it had never seemed to fit them.
One other reason that you may not be comfortable with your name is because you may be in search of your identity. Your name just might not feel right as you entertain the idea of your true likes and dislikes.
It could be worse. I have a friend who named her child Bat. Her full name is even stranger, but somehow the child has grown into a beautiful Bat.