The first time "taking the Lord's name in vain" was written in the bible is Exodus 20:7, and is echoed again in Deuteronomy 5:11.

"Thou shalt not take the name of the Lord thy God in vain; for the Lord will not hold him guiltless that taketh his name in vain."

The original Hebrew text and word used for the word "vain" in Exodus 20:7 is "Shav" according to Strong's Concordance. This word specifically means:

shav; from the same as (related word) in the sense of desolating; evil (as destructive), lit. (ruin) or more. (espec. guile), fig. idolatry (as false, subj.) uselessness (as deceptive, obj.; also adv. in vain):--false (-ly), lie, lying, vain, vanity.

Strong's Concordance - ISBN 0-7852-1195-0

As defined above, "using the Lords Name in vain" has more to do with lying, guile, idolatry (believing in a god other than than the "one true god", which could be believing in a version of God inaccurate of who He is because you like your own version better), uselessness, and being false. I would very much define saying one identifying as Christian, yet not living and acting like one as the ultimate exercise in uselessness and hypocrisy.

The Strong's Concordance has every word in the King James Version exhaustively identified with definitions of each. It is how theologians that aren't actually fluent in Greek or Hebrew can break apart a verse to find the true meaning that has been lost to dialect, translation, and the time. If you're interested, I would highly recommend finding one, or even downloading it.`

Here is a blog post that hits most of what I mentioned, and also has a few more things to consider.

One interesting thing of note is that, according to Leviticus 19:12, Christians are commanded to not bring shame upon their God by using him to swear falsely.

“Do not bring shame on the name of your God by using it to swear falsely. I am the LORD." -Leviticus 19:12

This implies that there are ways and times where it may actually be appropriate to use the Lord's name, or your association to him as a Christian, to swear if something is true. However, Jesus recommends or commands in the New Testament that no one swear by anything, either by God or anything else, and to let only your "yes be yes, and your no be no" lest one brings judgement upon themselves.

"But let your ‘Yes’ be ‘Yes,’ and your ‘No,’ ‘No.’ For whatever is more than these is from the evil one” -Matthew 5:37

And here is one more final thing to think about. In Christianity, God is perfect and without sin. If he were to sin in any way, by definition he would fall under the law of death, as death is the punishment for sin. Jesus, as an aspect of God, was also blameless and without sin. Many also believe the Bible to be the literal or interpreted word of God, such that any changes throughout time were foreseen and anticipated. I have my own views on this, but for the sake of my argument, we must assume the entire scripture to be God-breathed. If God cannot sin, and the bible must therefore be truthful, then how did God swear by using his own name, if swearing by his own name is sinful?

"For when God made a promise to Abraham, because He could swear by no one greater, He swore by Himself” -Hebrews 6:13

Therefore, either God sinned by using his own name in vain and cannot be god, God sinned by lying about it in the literal word of God in Scripture, or swearing by using the name of God or its derivatives is not inherently sinful, and the intent or veracity is what is judged.