It may be helpful first to understand exactly what is mean by the word "vain." The NOAD defines vain as "producing no result, useless" and "having no meaning or likelihood of fulfillment." The use of God's name is usually reserved for prayer. Calling upon God is meant to have some kind of effect, but only if the caller is penitent and sincere. If the use of God's name is not intended to produce such an effect, then it is used in vain.
George Q. Cannon, a former Counselor in the First Presidency of the Church, stated the following:
“Do angels take the Lord’s name in vain? The idea is so ridiculous
that we scarcely like to ask the question. … How dare we do that which
angels dare not do? Is it possible for us to argue that that which is
forbidden in heaven is praiseworthy on earth? …
“Though we are sure no boy can tell us any advantage that can arise
from the abuse of God’s holy name, yet we can tell him many evils that
arise therefrom. To begin, it is unnecessary
and consequently foolish; it lessens our respect for holy things and
leads us into the society of the wicked; it brings upon us the
disrespect of the good who avoid us; it leads us to other sins, for he
who is willing to abuse his Creator is not ashamed to defraud his
fellow creature; and also by so doing we directly and knowingly break
one of the most direct of God’s commandments”
The instructions from the First Presidency and the Quorum of the Twelve apply to the Church in the entire world, regardless of culture. In no culture is it acceptable to use the name of God lightly.
It should be clear that while invoking God's name without real intent is not acceptable, it is acceptable to respectfully reference God by name in a conversation.
Additional information may be found in this talk by former President Gordon B. Hinckley of the Church.