In Sunday School today, I was given a little more insight to this commandment. When we are baptized into the Church of Jesus Christ, we are also covenanting to take upon the name of Jesus Christ. We renew this covenant with Him every Sunday when we partake of the sacrament.
"O God, the Eternal Father, we ask thee in the name of thy Son, Jesus Christ, to bless and sanctify this bread to the souls of all those who partake of it; that they may eat in remembrance of the body of thy Son, and witness unto thee, O God, the Eternal Father, that they are willing to take upon them the name of thy Son, and always remember him, and keep his commandments which he has given them, that they may always have his Spirit to be with them. Amen." (Book of Moroni 4:3, Doctrine and Covenants 20:77)
To me that means, that when we fail to keep the commandments and go against the word of God, we are also taking His name in vain.
Perhaps everyone else already realized this, but to me, this is new and profound. It is not something I've ever thought of before. How grateful I am to have the Atonement, for the sacrament, and for Jesus Christ, so that when I do take God's name in vain, I can be forgiven.